Jesus' "Great Commission" to his (all male Apostles) was to "Go therefore and make disciples of all the nations, baptizing them in the name of the Father and of the Son and of the Holy Spirit, teaching them to observe all things that I have commanded you; and lo, I am with you always, even to the end of the age."
1) Jesus gave this great commission and teaching authority to his Apostles.
2) Jesus chose only males as His Apostles. He could have chosen women (He is God, after all), but He didn't.
3) Bishops (and to a lesser extent, priests) are successors to the Apostles.
4) Male bishops have Apostolic teaching authority (that extends down to priests to a lesser degree).
5) Therefore, the Church concludes that only priests have the authority to preach (/teach) during Mass.
You know, the claim by some misguided souls that women don’t have any real power in the Catholic Church is really amusing to me. Ask all the Teresa’s that come to mind. Let’s see, there’s the Doctors of the Church, Mother Teresa, hmmm.
Mother Angelica comes to mind, boy she never backed down from what she wanted to accomplish, did she.