Objection 1. It seems that the consecration of this sacrament does not belong exclusively to a priest. Because it was said above (Question 78, Article 4) that this sacrament is consecrated in virtue of the words, which are the form of this sacrament. But those words are not changed, whether spoken by a priest or by anyone else. Therefore, it seems that not only a priest, but anyone else, can consecrate this sacrament.
Objection 2. Further, the priest performs this sacrament in the person of Christ. But a devout layman is united with Christ through charity. Therefore, it seems that even a layman can perform this sacrament. Hence Chrysostom (Opus imperfectum in Matth., Hom. xliii) says that "every holy man is a priest."
Objection 3. Further, as Baptism is ordained for the salvation of mankind, so also is this sacrament, as is clear from what was said above (74, 1; 79, 2). But a layman can also baptize, as was stated above (67, 3). Consequently, the consecration of this sacrament is not proper to a priest.
Objection 4. Further, this sacrament is completed in the consecration of the matter. But the consecration of other matters such as the chrism, the holy oil, and blessed oil, belongs exclusively to a bishop; yet their consecration does not equal the dignity of the consecration of the Eucharist, in which the entire Christ is contained. Therefore it belongs, not to a priest, but only to a bishop, to perform this sacrament.
On the contrary, Isidore says in an Epistle to Ludifred (Decretals, dist. 25): "It belongs to a priest to consecrate this sacrament of the Lord's body and blood upon God's altar."
I answer that, As stated above (78, 1,4), such is the dignity of this sacrament that it is performed only as in the person of Christ. Now whoever performs any act in another's stead, must do so by the power bestowed by such a one. But as the power of receiving this sacrament is conceded by Christ to the baptized person, so likewise the power of consecrating this sacrament on Christ's behalf is bestowed upon the priest at his ordination: for thereby he is put upon a level with them to whom the Lord said (Luke 22:19): "Do this for a commemoration of Me." Therefore, it must be said that it belongs to priests to accomplish this sacrament.
Reply to Objection 1. The sacramental power is in several things, and not merely in one: thus the power of Baptism lies both in the words and in the water. Accordingly the consecrating power is not merely in the words, but likewise in the power delivered to the priest in his consecration and ordination, when the bishop says to him: "Receive the power of offering up the Sacrifice in the Church for the living as well as for the dead." For instrumental power lies in several instruments through which the chief agent acts.
Reply to Objection 2. A devout layman is united with Christ by spiritual union through faith and charity, but not by sacramental power: consequently he has a spiritual priesthood for offering spiritual sacrifices, of which it is said (Psalm 1:19): "A sacrifice to God is an afflicted spirit"; and (Romans 12:1): "Present your bodies a living sacrifice." Hence, too, it is written (1 Peter 2:5): "A holy priesthood, to offer up spiritual sacrifices."
Reply to Objection 3. The receiving of this sacrament is not of such necessity as the receiving of Baptism, as is evident from what was said above (65, 3,4; 80, 11, ad 2). And therefore, although a layman can baptize in case of necessity, he cannot perform this sacrament.
Reply to Objection 4. The bishop receives power to act on Christ's behalf upon His mystical body, that is, upon the Church; but the priest receives no such power in his consecration, although he may have it by commission from the bishop. Consequently all such things as do not belong to the mystical body are not reserved to the bishop, such as the consecration of this sacrament. But it belongs to the bishop to deliver, not only to the people, but likewise to priests, such things as serve them in the fulfillment of their respective duties. And because the blessing of the chrism, and of the holy oil, and of the oil of the sick, and other consecrated things, such as altars, churches, vestments, and sacred vessels, makes such things fit for use in performing the sacraments which belong to the priestly duty, therefore such consecrations are reserved to the bishop as the head of the whole ecclesiastical order.
Source: Summa Theologica (New Advent)