Why can't the laity preach a homily, and can a lay person ever preach? From this, Rochester diocese ends illicit practice of allowing lay people to preach homilies, perhaps because this was going on for such a long time, a person would ask what is the authoritative Catholic Church Teaching that prohibits a lay person (of either gender) from preaching the homily at Mass and are there cases where the laity may (men or women) can be allowed to preach in a church or oratory? Under what circumstances?
Code of Canon Law states:


  766.0 Lay persons can be permitted to preach in a church or oratory, if necessity requires it in certain circumstances or it seems advantageous in particular cases, according to the prescripts of the conference of bishops and without prejudice to 767.1 
  
  767.1. Among the forms of preaching, the homily, which is part of the liturgy itself and is reserved to a priest or deacon, is preeminent; (....)


So, non-ordained faithful can preach, but NOT in the Mass. Because homily in the mass is a part of the liturgy which is reserved to the cleric (priest and deacon) alone. The reason for this is answered in Instruction On Certain Questions Regarding The Collaboration Of The Non-Ordained Faithful In The Sacred Ministry Of Priest Article 3.1


  The homily, therefore, during the celebration of the Holy Eucharist, must be reserved to the sacred minister, Priest or Deacon(69) to the exclusion of the non-ordained faithful....  This exclusion of the lay people is not based on their preaching ability of sacred ministers nor their theological preparation, but on that function which is reserved to them in virtue of having received the Sacrament of Holy Orders. For the same reason the diocesan Bishop cannot validly dispense from the canonical norm since this is not merely a disciplinary law but one which touches upon the closely connected functions of teaching and sanctifying.



PS: 'The homily should ordinarily be given by the priest celebrant himself. He may entrust it to a concelebrating priest or occasionally, according to circumstances, to the deacon, but never to a lay person. In particular cases and for a just cause, the homily may even be given by a bishop or a priest who is present at the celebration but cannot concelebrate.' (GIRM 66)