The feminist movement has made a lot of hype about ordaining women into the priesthood, going as far as to say the Church is sexist and discriminates women for not having priestesses. There is even a group of Catholics called WomenPriests whose goal is to ordain women into the priesthood.
The main issue is this: ordination is not a right, it is a vocation from God which is not for everybody. As the Catechism says, “No one has a right to receive the sacrament of Holy Orders” (no. 1578). It is not for us to say who may be ordained and who cannot. It continues saying, “The Lord Jesus chose men (ver) to form the college of the twelve apostles, and the apostles did the same when they chose collaborators to succeed them in their ministry” (ibid). We see this continuity. Many like to say Jesus was just following the culture of His time, but the problem is Jesus was known for being a rebel: He called the Pharisees “brood of vipers”, “hypocrites”, “whitewashed tombs”, and He called Herod “that fox”, and He expelled the moneychangers from the Temple, He told the Pharisees that food does not defile the body but that which comes from within which we call immorality. Furthermore Jesus Christ promised that the gates of Hell could never prevail against the Church (rf. Matthew 16:18), and He gave her infallibility in matters of doctrine. We would have to anyways because we put our faith in the Church that the Canon of Scriptures we have is divinely inspired (rf. 2 Timothy 3:16); to not put faith in the Church regarding the priesthood is to misplace faith in the Church regarding the Canon.
Saint Paul said, “Let women keep silence in the churches: for it is not permitted them to speak, but to be subject, as also the law saith” (1 Corinthians 11:34). One of the priest’s roles is to preach the homily at Mass, but here we see women may not speak at Mass, so she cannot say the homily and thus she may not be a priestess. He adds, “But I suffer not a woman to teach, nor to use authority over the man: but to be in silence” (1 Timothy 2:12). The common rebuttal to this is that “there is neither male nor female” for all “are one in Christ Jesus” (cf. Galatians 3:28). Ex-President Jimmy Carter said this in an interview. This is really the liberal Protestant idea of taking Scripture passages as if they contradict each other so as to look for the ones they like. The passage is about justification by faith as is said, “But the scripture hat concluded all under sin, that the promise, by the faith of Jesus Christ, might be given to them that believe. . . For as many of you as have been baptized in Christ, have put on Christ” (v. 21-27). Now to think of it, it seems they use Galatians 3:28 to say there is no gender — hence taking the “neither male nor female” passage literally — so as to support gender theory and transgenderism and in the attempt to say we cannot say male priesthood alone; due to its very nature it is tied to the LGBT movement as well, but that will be left for another time. See for example the Episcopal Church in the United States: it ordains women, consecrates same-sex unions and supports gender theory and transgenderism. Other Protestant churches like the Presbyterian Church in the United States (PCUSA) are going in the same way since they already ordain women and/or consecrate gay unions.
So, is there a purpose for Christ ordaining men only? Yes, because the Mass is a marital banquet as we see in Revelation 19:19 as it says, “Blessed are they that are called to the Supper of the Lamb.” This is repeated at every Mass. Christ was incarnate as Man, not a woman, and as mentioned earlier the priest acts in persona Christi. Thus it is fitting: Christ is masculine and His Church is feminine; Christ is the head of His Church just as the husband is the head of his wife as Saint Paul says (rf. Ephesians 5:23). He offered Himself for the Church and continues so through the priest who offers the Body and Blood for the Church.
Saint John Paul II defined this dogma: “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” (Ordinatio Sacerdotalis, no. 4). Even before this “ordained” women were excommunicated along with their minister of ordination although such an attempt was rare. It should be noted the priestesses are a pagan concept: just look at Wiccans, ancient Egyptians, Greeks and Romans or African tribes. The Lord warned, “Learn not according to the ways of the Gentiles” (Jeremias 10:2). In the second century we already see a clear reference to a uniquely male priesthood.
“Pretending to consecrate cups mixed with wine, and protracting to great length the word of invocation, [Marcus the Gnostic heretic] contrives to give them a purple and reddish color. . . . [H]anding mixed cups to the women, he bids them consecrate these in his presence.” ~ Saint Irenaeus (Against Heresies 1:13:2).
“It is not permitted for a woman to speak in the church [1 Cor 14:34–35], but neither [is it permitted her] . . . to offer, nor to claim to herself a lot in any manly function, not to say sacerdotal office.” ~ Tertullian (The Veiling of Virgins 9)