...from the article "A Sociologist Against Women's Ordination" by David R. Carlin (which can be found online). David R. Carlin is the author of Can a Catholic Be a Democrat? and The Decline and Fall of the Catholic Church in America.
After pointing out that Catholicism has often been labelled as a "feminine" religion, that it tends to prioritize "feminine" virtues such as self-control and compassion, he puts the question:
"If women have more of an aptitude than men for Christian sanctity, doesn't that mean that they are called more than men to the priesthood?" I don't know whether they are more "called" or not, but their aptitude for Christian sanctity is precisely the reason, as I see it, that they should be kept out of the priesthood. For if women were to be ordained, they would soon – within 50 years, I'd guess – become overwhelmingly predominant in the priesthood. Female priests would outnumber male priests by ten or 20 to one, if not more. Catholicism would be perceived, and correctly so, not just as a "feminine" religion but as a female religion. Males would pretty much abandon it.
I don't know why Christ chose twelve male Apostles. I don't know why the Holy Spirit has led the Church to confine the priesthood and episcopacy to men, especially when women can evidently live lives of heroic virtue just as well as any man, and can even be Doctors of the Church like Saint Teresa of Avila.
I do perceive from the Gospels, though, that our Lord showed a marked reluctance to explain his choices, for instance in the epilogue to the Gospel of St. John.