For well over a millenium, the Catholic Church has taught that women cannot be ordained. The latest position paper on the subject, Inter Insigniores is a piece of crap which:
Admits that one of the main reasons for denying ordination to women has been the attitude that women were inferior to men and says that this argument should be abandoned but then resurrects it without admitting it's doing so.
To expand on this last, see, for example, Thomas Aquinas, Summa Theologica Supplement, question 39 article 1, which considers the question, "Whether the female sex is an impediment to receiving Orders?". He says that it is, for two reasons. The first is that women are inferior to men ("since it is not possible in the female sex to signify eminence of degree, for a woman is in the state of subjection, it follows that she cannot receive the sacrament of Orders"
. The Vatican has officially repudiated this argument.
The second reason is: "Further, the crown is required previous to receiving Orders, albeit not for the validity of the sacrament. But the crown or tonsure (a ritual shaving of the head) is not befitting to women according to 1 Cor. 11. Neither therefore is the receiving of Orders." Now, he admits that the tonsure is not required for the validity of the sacrament. Indeed, the tonsure is not performed nowadays. Thus, this reason, which was shaky in Aquinas' day, no longer is a real objection.
Relies on the extremely dubious argument that Christ ordained only men to the priesthood, therefore women cannot be ordained. First, even if you grant this argument, one can just as reasonably say that since Christ ordained only Jews to the priesthood, gentiles should not be priests. But the fact is that Christ did not "ordain" anyone.
Makes the really silly argument that since the priest is supposed to "mirror Christ", the laity would not be able to see Christ in a woman. I daresay that the laity would be far less likely to see Christ in a pedophile. This argument also shows the Vatican's basic contempt for the laity.
Finally, Pope John Paul II attempted to quell discussion in his Ordinatio Sacerdotalis -- "On Priestly Ordination", which can be summed up as "Women cannot be ordained because I say so. Now sit down and shut up!" This argument may work with very small children (but don't count on it), but it only convinces those who believe that every burp which issues from a papal throat is the word of God. They shouldn't expect any adults to buy it.
JPII also put out a document, Mulieries Dignitatem -- "The Dignity of Women" -- which speaks of the "complementarity" of men and women, saying that there are "ontological differences" between the sexes. Exactly what these ontological differences are and how they preclude women from being ordained is more than a bit vague. I believe that this is nothing more than the discredited inferiority argument, tarted up with philosophical gobbledygook and with a new coat of paint over the dry rot. JPII writes as if denying ordination to women was a good thing for women, which reminds me of some pre-Civil War pro-slavery types who tried to say that slavery benefitted the slave.