I found this to be a very good article on an issue that people often ask me about:
Significantly, from the article:
The meaning of the Mass is encapsulated in the words the priest says as he pours the water and wine into the sacred chalice: “Through the mystery of this water and wine may we come to share in Christ’s divinity who humbled himself to share in our humanity.”
Now the reason for preaching being reserved to priests and deacons becomes clear. At the Mass the priest and the deacon stand in persona Christi. They represent Christ symbolically and liturgically, one as Christ the Priest, the other as Christ the servant.
This is why they are ordained. NOT just to be a social worker in black. Not just to be a theology teacher in a collar. Not just to be a spiritual director or a parish administrator or a fund raiser.
The priest and deacon are ordained and set apart from the laity for this reason: to help incarnate Christ in the world through their own person and through their own vocation. This is why the catechism teaches that one of the ways to objectively know that you have encountered the risen Lord is “in the person of the priest.”
Lay people can’t do that in the same way, and that’s why they are not permitted to preach at Mass.