As Catholics, we believe in an incarnational and sacramental view of the world. This means matter is not incidental. God created it good for a reason and redeemed it by assuming to Himself a physical human nature. Our bodies and our genders are not incidental. They are essential components of who we are (components is the wrong word: we are body soul composites). God works through matter. When God became a man it was not by accident, but by choice. Christ’s maleness was meant to reveal something to us about the relationship between God and His Church. There is also a good reason why God designed the Church to be female, and why He designed human beings to have gender in the first place. He designed us to be made for each other. He made us to be physically and emotionally complementary (this is one reason why the Church rejects homosexual acts).
The male represents transcendence (going beyond oneself); the female represents immanence (receiving and conceiving within oneself). The male gives; the female receives. The male should give everything that he is to his beloved. The female beloved should receive everything that her lover is. This is clearly modeled in the marital act, a sacramental action that makes present that fecundity, love, and union of which it is a sign.
Christ gives us everything He is in the Eucharist. We the Church (female) receive all that He is. The priest gives us the Eucharist. We receive the Eucharist. This shows the necessity of the priest being male if we are to have an adequate sign of the reality taking place. Remember, we are incarnational and sacramental, so the SIGN IS IMPORTANT!
This does not mean women are of less value or dignity than men. It only means that men and women (who are both made in the image and likeness of God) have different roles in the Body of Christ. The eye should not say to the hand, “I do not need you, or I wish I was like you.” Each person should fulfill his or her calling in life according to his or her God-given nature. Each person should strive to play the role God has given them to play in the building up of the Body of Christ.
Jesus loved His mother more than anyone; if priesthood was based on holiness, Mary would have been the first priest. Jesus went against cultural norms in many ways (calling Himself “I AM”). If women were to be priests, He would have made it so by naming a woman to be one of the twelve. There were already many priestesses in the ancient world. It would have been shocking within Judaism, but then again, so would the Incarnation and Trinity.
Hope this helps.