66. 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.65 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.
Redemptionis Sacramentum, promulgatged in 2004 by no less than the Venerable Pope John Paul II (and, written, in part, by the former Joseph Cardinal Ratzinger when he was Prefect for the Congregation for the Doctrine of the Faith) goes into greater detail:
[64.] The homily, which is given in the course of the celebration of Holy Mass and is a part of the Liturgy itself,142 "should ordinarily be given by the Priest celebrant himself. He may entrust it to a concelebrating Priest or occasionally, according to circumstances, to a Deacon, but never to a layperson.143 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".144
[65.] It should be borne in mind that any previous norm that may have admitted non-ordained faithful to give the homily during the Eucharistic celebration is to be considered abrogated by the norm of canon 767 §1.145 This practice is reprobated, so that it cannot be permitted to attain the force of custom.
[66.] The prohibition of the admission of laypersons to preach within the Mass applies also to seminarians, students of theological disciplines, and those who have assumed the function of those known as "pastoral assistants"; nor is there to be any exception for any other kind of layperson, or group, or community, or association.146
I highlighted this particular section because seminarians are not yet ordained. While the intention may be to either give them some time to learn homelitics, the Holy Sacrifice of the Mass is not the venue for this kind of training.
I write this because a friend of mine called me after having attended Mass at her parish. She told me that the pastor had read the Gospel, but, then, invited one of the seminarians to talk about Our Lady of Guadalupe during the time reserved for the homily. The priest did not preach at all. I told her that this was ilicit. Redepemptionis Sacramentum goes so far as to say that this practice is reprobated. She told me that the seminarian did a good job; however, even if he were to preach like St. Paul, that does not take away the fact that he should not have been preaching at all. The Church is very clear about the fact that the celebrant or the deacon should be the one preaching a homily on Sunday.
Now, regarding the seminarian (or any other lay person), RS does state the following:
[161.] As was already noted above, the homily on account of its importance and its nature is reserved to the Priest or Deacon during Mass.260 As regards other forms of preaching, if necessity demands it in particular circumstances, or if usefulness suggests it in special cases, lay members of Christ's faithful may be allowed to preach in a church or in an oratory outside Mass in accordance with the norm of law.261 This may be done only on account of a scarcity of sacred ministers in certain places, in order to meet the need, and it may not be transformed from an exceptional measure into an ordinary practice, nor may it be understood as an authentic form of the advancement of the laity.262 All must remember besides that the faculty for giving such permission belongs to the local Ordinary, and this as regards individual instances; this permission is not the competence of anyone else, even if they are Priests or Deacons.
Thus, the seminarian could have very well delivered his reflection, but, not within the confines of the Mass. My friend told me that the parish was going to have a play depicting the Guadalupe apparitions tomorrow morning. I told her that this would have been the most appropriate setting for such a talk.
What is sad is that both the pastor and the seminarian should have known better. The priest is obligated, by both the character of Holy Orders and by Church liturgical law, to preach a homily on Sundays. Now, he could have entrusted this to a deacon if he was unable to preach, but, never, never to a lay person. Seminarians are not ordained. Thus, they are laity. Even duly instituted alcolytes are not allowed to preach.
Redemptionis Sacramentums specifically states that the faithful have the right to a properly celebrated Holy Sacrifice of the Mass. That is to say that it must be free of abuse. Not preaching a homily and handing over this task to a seminarian is a serious abuse to the point that the Church calls this practice reprobate.