Why can't women be priests?

Before we discuss the main reason why (which has nothing whatsoever to do with any kind of superiority of men), it will be helpful to show that Pope John Paul II has definitively told us that the male priesthood is part of the faith itself:

"Although the teaching that priestly ordination is to be reserved to men alone has been preserved by the constant and universal Tradition of the Church and firmly taught by the Magisterium in its more recent documents, at the present time in some places it is nonetheless considered still open to debate, or the Church's judgment that women are not to be admitted to ordination is considered to have a merely disciplinary force.  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. Lk 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" (Ordinatio Sacerdotalis).

The Church teaches that Jesus chose only men to be Apostles, and that He was not limited to His time in doing so.  It has also often been pointed out that there were many women priests around the Mediterranaean in Jesus' day, and He could have followed that practice without losing His followers.  Even if that were not the case, Jesus often proved Himself willing to offend the sensibilities of the people of His time, including if it meant losing His followers, as in the case of His teaching on the Eucharist in John 6, where most forsook Him because of His controversial teaching.

But these remarks and ones along these lines only show that the male priesthood was Jesus' sovereign intent, and do not explain His actual reason for the limit.  I would like to propose something that is simply my own view as to why, and I got it from an idea that appeared in Peter Kreeft and Alice Von Hildebrand's book Women and the Priesthood, published by Franciscan University Press.  This view is neither specifically taught nor denied by the Catholic Church, and may be accepted or not given how it seems reasonable to the reader.

On the whole, men stand more in need of the Gospel message than women.  Men have greater hormonal aggression, as we see when they take male steroids and become more violent, short-tempered, and so on.  In the animal kingdom, the widespread fighting contests for male dominance bear a striking resemblance to human male behavior in adolesence and later.

Christianity, by contrast, teaches that we should be meek and serve others. Jesus calls Himself a servant, and washes the feet of the Apostles (a deeply humbling thing for a Jewish person to do at the time).  Christians are called to turn the other cheek, love the weak and downtrodden, and nurture the elderly. Historically, then, women have been, in a word, more Christian than men have, when looking at each gender as a whole.

The reasons for this are fairly clear.  Women's physiology, from pregnancy to breast-feeding, means a usually closer bond to defenseless children, even apart from whatever maternal instinct comes into play.  Society comes to reinforce these roles in women, and so even those women who do not give birth to children (or who have not yet done so) are more likely to have a Christian way of behaving encouraged in them than men.  While men are completely capable of kind behavior and find their true happiness in it, their biology has many times been a hindrance to their doing so.  Christian masculinity should be prized, and it does not mean that the Christian man must become feminine -- only that men require a greater call to live the life of Christian meekness.

With a male-only priesthood, men are given a constant reminder that their gender can live the Christian life and be valued in doing so.  Women have been more prevalent at Christian churches throughout history, but the male priesthood helps act as a countermeasure.  In a real sense, then, the male priesthood has to do with a sort of extra effort that men require, and so has nothing to do with domination by one gender over the other.

Such a view also explains why, when God became human, He chose to come as the gender that required the more earnest call.