Given that a tiny group of ecclesial dinosaurs here in the U.K. are plastering London buses with pro-WO ads, I thought it might be time to revisit the issue in some detail.
Below is a piece I posted back in 2008 at the request of a young  Dominican friar who was asked about the Church's teaching on the  impossibility of women's ordination to the Catholic priesthood.
It's long, but I promised detail, right?!
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First, notice  the origin and ground of the objections.  All of them are based on one  or more  of the following mistakes:
a)  Priesthood is about power
b)   "Access" to the priesthood is about rights and justice
c)  The  "exclusion" of women from the priesthood denies humanity of women. . .
d)   . . .and it denies their proper place as potential "Christs for  others"
e)  All exercises of Church authority are excluding
f)   Tradition is always about male privilege
g) Women would make better  priests because of their natural empathy and compassion
h)  Jesus'  exclusion of women from the priesthood was culturally based and  therefore reformable
i)   Scripture is silent on the nature of the  priesthood b/c it is a third century invention of males
j).  Women  report feeling called to the ordained priesthood, therefore the Church  ought to ordain them.
Let's answer (briefly) each in turn.
Priesthood  is about power.  No, it's not.  Priesthood in the Catholic  Church is about service.  Do priests often mistake their office of  service as a privilege in the use of power?  Yup.  But that's an abuse  of the office and in no way changes the actual nature of the office.    Men are ordered to Christ, Head of the Church, to serve his people as he  did:  sacrificially in leadership.  When supporters of women's  ordination (WO) claim that women must be allowed to share in the  governance of the Church as priests, they mistake the office for a  political one.
"Access" to  the priesthood is about rights and justice.  Wrong again.  The  only right a Catholic has as a Catholic in the Church is the right and  duty to serve others.  Justice is getting what one deserves.  No  one--not even men--"deserve" to be ordained, to serve as ordained  priests.  To claim that ordination is a right is bizarre given that men  are called by God and confirmed by the Church to be priests.  This use  of democratic rhetoric is attractive but misplaced.  You cannot be the  subject of an injustice if you have no right to that which you have been  denied.  I am not being treated unjustly b/c I cannot vote for the next  Italian presidential election. 
The "exclusion" of women  from the priesthood denies their humanity.  In fact, the Church's  teaching on ordination reaffirms the humanity of women by clearly  laying out what it means to be human, male and female.  To be fully  human as a creature is to submit one's will to the will of our Creator  and cooperate with His grace to achieve our perfection AS men and women;  that is, I am perfected as a male creature.  My mother is perfected as a  female creature.  Often this objection is rooted in a modernist notion  that one's sex is socially constructed.  We are MADE male and female by  our Creator and not pieced together sexually by social forces.
The "exclusion of women from the  priesthood denies their proper place as potential "Christs for others."   This would be true if the only means of being Christs for others was  to be a priest.  Fortunately, our Lord had to foresight to make sure  that there were other means of becoming the sons and daughters of the  Father in His service for others.  Ordination is one way that some men  are called by God and confirmed by the Church to "work out" their  salvation.  No one is denied their perfection in Christ b/c they are not  priests.  All the baptized serve the Father by being priests, offering  themselves in sacrifice for others.
All exercises of Church authority are excluding.  Wrong.   If an exercise of Church authority excludes, it does so in order to  liberate through a declaration of the truth of the faith., thus  including everyone in the knowledge of truth.    To be excluded is not  in and of itself an injustice or a violation of human dignity.  There  are many perfectly beautiful options open to all Christians to which I  am excluded in virtue of my ordination, e.g. marriage and biological  fatherhood.  In the case of WO, the Church has used her authority to  recognize a limit of her own power.  In effect, the Church has  recognized that she is excluded from considering the ordination of  women.
Tradition is always  about male privilege.  Tradition has certainly been misused to  prop up abusive practices that privilege males.  That we have seen these  abuses in no way changes the fact that Tradition is the handing on of a  living faith, the "living faith of the dead."  The faith of the Church  never changes.  It cannot change.  Our understanding of the faith can  and does change.  However, WO is not a change in understanding but a  radical revision of some of the most basic threads of the Christian  narrative.  To alter these threads does more than "open the priesthood,"  it unravels the faith whole clothe.
Women would make better priests.  I concede this  readily.  But we have to be clear about what we mean by "better  priests."  The objection assumes that the vocation of the priest is  simply about empathy and compassion.  It's not.  Sometimes what the  priest must do is show firmness, rectitude, and unwavering direction. .  .even if empathy and compassion seem to be set aside in doing so.  If  the only vocation of the priest were to be empathetic or compassionate,  then women should be ordained.  However, as we have seen in the  Episcopal Church and the Church of England, women priests and bishops  (at least for now) seem to be more inclined to the destruction of the  living faith than its preservation.  Each time a stone in the catholic  faith has been removed by female clergy and their male supporters in  these ecclesial communities, it has been removed on the grounds of  justice, rights, empathy, and compassion--all understood in strictly  secular terms.  The results have been disastrous.
Jesus' "exclusion" of women from the  priest was culturally based and therefore reformable.  This  objection assumes as true a number of false premises.  First, it assumes  that Jesus was not who he clearly said he was and is:  God.  God is not  constrained by cultural prejudices.  Second, it assumes that Jesus was  disinclined to break social taboos.  In fact, he broke any number of  cultural taboos in teaching and preaching the Good News, causing a great  deal of scandal.  Why not break the taboo against women as  priests/rabbis?  Third, this objection also assumes that cultural change  should guide Church teaching.  Cultural change should and often does  guide our understanding and application of the faith in the world, but  the world is irrelevant when it comes to determining the content of our  faith.  A danger for WO supporters here is that the way they understand  many of the Church's cherished social justice positions are undermined  by this objection to the Church's teaching.  If we can alter the faith  to follow cultural change and ordain women, why can't we examine many of  Jesus' legitimate justice teachings in the same light and alter them as  well?  Maybe our modern culture and social norms should be used to  override the historical Christian concern for the poor.   Surely, the  recent collapse of the economy can be blamed in part on a misplaced  concern for the poor and homeless.
Scripture is silent on the nature of the priesthood.   This is a particularly odd objection for faithful Catholics to be  making.  It is largely a Reformation objection and ignores volumes of  Patristic teaching on the origins and development of Christian  priesthood.  It is simply false to say that the Catholic priesthood is  an third or fourth century invention.  There are elements of the  priesthood as it is enacted in the world that came about in later  centuries, but the core nature of the priesthood was infallibly  established at the Last Supper when Christ commissioned his apostles and  friends as those who would lead the community in prayer and the  breaking of the bread, to "do this in memory of me."  He had every  opportunity to include women in this moment, but he didn't.  The key  here is to understand that the Last Supper was a Passover meal, a family  meal, one that reinforced the bonds of paternal authority in the  ancient Jewish tradition. of liberation from slavery.  Even with women  present at a Jewish Passover, the men are commissioned to perform the  rite.  Does this mean that women are excluded from the liberation Moses  brought and the Passover celebrates?  Hardly.
Women feel called to the priesthood.  In the  paragraph directly below this one I note that all of the objections to  the Church's teaching on WO are rooted in modernist, feminist ideology.   This objection is a perfect example.  What this objection assumes is  that the call to priesthood is a subjective experience immediately  deserving a positive response from the Church.  What can be more  modernist than the triumph of personal experience over objective truth.   The truth of the matter is that the call to priesthood comes from God  through the Church, who is the Body of Christ.  To say that a particular  person (male or female) receives a call outside the Church assumes that  Christ speaks to a member of his Body from outside his Body.  However,  all calls to serve the Body come through the Church and are therefore  verifiable by the Church.  Most of us believe we are called to all sorts  of vocations for which we do not have the requisite gifts or authentic  vocation.  I feel called to be a regularly published poet, yet my poetry  is regularly rejected.  The poetry community (i.e., the Church of  Verse) regularly rejects my claims to being a poet.  Years of personal  experience, strong conviction, earnest effort, and multiple academic  degrees cannot make up for the lack of consent by the poetry community  to my alleged call.  I can call myself a poet.  I can rail against the  perceived injustice of not being regularly published.  I can even accuse  my tormenters of bias, hatred, and lack of taste.  I'm still not a  poet.  Think for a moment of the implications if the Church bowed to the  "I feel called to priesthood" objection and answered these claims  positively.  On what grounds could we reject anyone from the ordained  ministry?  My application to be made a postulant for ordination in the  Episcopal Church was rejected.  Had the vestry of my parish not done  their job of proper discernment and oversight, I would be an  Episcopalian priest right now.  Thank God they listened to the Holy  Spirit!
It is important for faithful Catholics to understand how  many of these objections are based on modernist, feminist theories of  justice, gender, the social construction of reality, and postmodern  identity politics.  None of which have a place in the faith of good  Catholics.  All are deeply rooted in 19th and 20th century liberal  democratic ideas about freedom, liberty, and rights.  None of them pull  from the tradition of the Church or her ancient philosophy and theology.   None of them are scriptural or magisterial.  I have yet to read a  single objection to the Church's infallible teaching against WO that  does not rely exclusively on ideas and argument entirely alien to our  faith.   The canonical objections I've read are little more than  legalistic sophistry and grounded in a "hermeneutic of suspicion" that  starts with an antagonistic attitude toward truth and quickly devolves  into relativism and subjectivism--little more than minute loopholes.
Probably  the best book on this subject was written by Sr. Sara Butler, MSBT, 
The Catholic Priesthood and Women: A Guide  to the Teaching of the Church,  Sr. Sara started her life as a  religious as a supporter of WO and has since looked carefully at the  scriptural, tradition, magisterial, and archeological evidence for that  position and changed her mind.  This book does a much better job of  defending the Church's teaching than I ever could, and I highly  recommend it.
It is vitally important that women understand that  the Church's lack of authority to ordain them to the priesthood is not  based on the notion that they are inferior or damaged or in any way  "less than men."  Yes, some medieval theologians, including Thomas  Aquinas, put forward certain metaphysical explanations for an all-male  priesthood that few of us will applaud now.  But these are merely  explanations of any already existing teaching and their dubious nature  in no way detracts from the truth of the faith.   In other words,  Aquinas, et al did not invent the all-male priesthood based on medieval  notions of biology and metaphysics.  They took up the question in light  of the sacaramental theology then current and the already existing  reality of the all-malle priesthood and attempted to explain the truth  of the priesthood in the light they had.  Demolishing Aquinas' argument  for the all-male priesthood does not demolish the Church's infallible  teaching against WO.
A note on the question of the infalliablity  of Pope John Paul II's document, 
Ordinatio  Sacerdotalis. This 1994 document was issued by the Holy  Father in order to settle forever the question of whether or not the  Church has the authority to ordain women.  Drawing on scripture,  tradition, and centuries of papal magisterial teaching, he concluded  that the Church does not have the power to ordain women.  It is very  important to understand that the Pope did not say that the Church will  not ordain women or that the Church does not feel like ordaining women.   He wrote:  "I declare that 
the Church  has no authority whatsoever to confer priestly ordination on  women. . ."  The Church CANNOT ordain women.  The Church also cannot  declare that Jesus is not the Savior.  The Church cannot declare that  Mary was not the mother of Jesus, etc.  In other words, the failure of  the Church to ordain women is not based on a lack of will or inclination  or patriarchal prejudice.  If every bishop in the Church, including the  Pope, laid hands on a woman, performing the entire sacrament of  ordination on her in St Peter's Bascilica in front of the College of  Cardinal with their wild applauses, she would still be a laywoman.   And  she would be a laywoman if every Catholic in the world believed that  she was a priest.
Is this teaching infallible?  Yes, it is.  The  Pope wrote in full: "Wherefore, in order that all doubt may be removed  regarding a matter of great importance, a matter which pertains to the  Church's divine constitution itself, in virtue of 
my ministry of confirming the brethren  (cf. 
 Luke 22:32) I declare that  the Church has no authority whatsoever to confer priestly ordination on  women and that this judgment is to be  definitively held by all the Church's faithful."
Now, some  theologians claim that this teaching is not infallible.  They want to  make a fine distinction between the content  of the teaching and this declaration  of the teaching.  They want to say that OS itself is not infallible; in other words, they want  us to believe that the Pope's declaration that the teaching is  infallible is not itself infallible.  This is typical modernist  sophistry and a confusion of terms.  All the Pope did in this document  is repeat an ancient truth:  women cannot be ordained.  This is not new.   Imagine the Pope issuing a document tomorrow declaring that Jesus is  the Messiah.  Such a document would be pointless because the Church has  always believed this.  There is no need for an infallible teaching on  the question.  How odd would it be then for some theologians to assert  that the document is not infallible when it asserts that the teaching  that Jesus is the Messiah is infallible.  Simply bizarre.
Reread  the highlighted phrases above.  Those are the words required for an  infallible teaching.  Period.  OS  as a document, OS per se does  not have to be infallible, just as a document declaring Jesus as the  Messiah would not have to be infallible.  The content of the teaching is  without error regardless of the magisterial/canonical status of the  document.  What the supporters of WO want us to believe is that the Pope  is not interpreting the ancient teaching correctly.  That he is merely  repeating what has always been the case in the Church seems to be  irrelevant to them.  It seems odd to me that the Pope would issue this  document "so that all doubt might be removed" and then have some claim  that he did so in order to set the stage for future women's ordinations!   We had a professor in my seminary who taught exactly that.   Fortunately, none of us fell for the deception.
Fr. Joseph  Fitzmeyer, quoting a supporter of WO, Rev. Herman Pottmeyer,  "According to Pottmeyer, 'O.S. is an instance of ordinary (i.e.,  non-infallible) magisterium, declaring that the church’s unbroken  tradition with regard to ordination is irreformable.' In saying this, he  may be right, even though the Congregation for the Doctrine of the  Faith subsequently explained that the doctrine about women’s ordination  belongs to the deposit of faith and has been constantly held in the  church’s tradition and infallibly set forth by the ordinary and  universal magisterium."  Fr. Fitzmeyer concludes his critique of Rev.  Pottmeyer, "Pope John Paul II stated in O.S. that 'the church has no  authority whatsoever to confer priestly ordination on women' (No. 4). He  did not mean that 'he could not himself change tradition in this  matter.' He spoke rather of Ecclesiam  facultatem nullatenus habere. If it is so, that the church has no  ability to change it, then the Pope cannot invite everyone to prayer  and dialogue as he would summon 'a council to make a final decision.' If  'the church' cannot do it, then a council cannot do it, no matter what  'signs of the times' may be or what 'faithfulness to Jesus' might seem  to call for in Pottmeyer’s estimation."
Best book on the history  and theology of the Church's teaching authority:  Magisterium:  Teacher and Guardian of the Faith, Cardinal Avery Dulles, SJ.
This  link  from the USCCB helps to clarify a number of issues.
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