The key point is that the "matter" of the Sacrament of Holy Orders is a man, just as the "matter" of the Holy Eucharist is bread and wine. Both points are connected to the nature of the Eucharist. The Eucharist is the re-presentation of both the giving of Christ's Body and Blood at the Last Supper, and of the Sacrifice of Christ on the Cross.
In this sacrifice, Christ is both Priest and Victim: He offers Himself to God the Father for us. The ministerial priest is mystically conformed to Christ Himself, and mystically participates in the (original) Last Supper and the Crucifixion. Because the priest is in place of Christ ("alter Christus"), and Christ was a man ... a real man, human flesh and blood and members and hormones and everything else ... the nature of the Eucharistic Sacrifice requires that the priest also be a man.
I think it is essential that we understand this theologically, because the Truth is True, independent of all other considerations. What "men" as a class or "women" as a class are like is irrelevant, particularly since almost all such generations are largely personal prejudice, rather than reality. The fact that the Apostles were all men is a useful guide, but it's not the key. The fact that "ordaining" women has been a first step toward catastrophe in many denominations is fascinating and instructive, but also not the main point.
Great answer, thanks.