Objection 1. It seems that Confirmation is not a sacrament. For sacraments derive their efficacy from the Divine institution, as stated above (Question 64, Article 2). But we read nowhere of Confirmation being instituted by Christ. Therefore it is not a sacrament.
Objection 2. Further, the sacraments of the New Law were foreshadowed in the Old Law; thus the Apostle says (1 Corinthians 10:2-4), that "all in Moses were baptized, in the cloud and in the sea; and did all eat the same spiritual food, and all drank the same spiritual drink." But Confirmation was not foreshadowed in the old Testament. Therefore it is not a sacrament.
Objection 3. Further, the sacraments are ordained unto man's salvation. But man can be saved without Confirmation: since children that are baptized, who die before being confirmed, are saved. Therefore Confirmation is not a sacrament.
Objection 4. Further, by all the sacraments of the Church, man is conformed to Christ, Who is the Author of the sacraments. But man cannot be conformed to Christ by Confirmation, since we read nowhere of Christ being confirmed.
On the contrary, Pope Melchiades wrote to the bishops of Spain: "Concerning the point on which you sought to be informed, i.e. whether the imposition of the bishop's hand were a greater sacrament than Baptism, know that each is a great sacrament."
I answer that, The sacraments of the New Law are ordained unto special effects of grace: and therefore where there is a special effect of grace, there we find a special sacrament ordained for the purpose. But since sensible and material things bear a likeness to things spiritual and intelligible, from what occurs in the life of the body, we can perceive that which is special to the spiritual life. Now it is evident that in the life of the body a certain special perfection consists in man's attaining to the perfect age, and being able to perform the perfect actions of a man: hence the Apostle says (1 Corinthians 13:11): "When I became a man, I put away the things of a child." And thence it is that besides the movement of generation whereby man receives life of the body, there is the movement of growth, whereby man is brought to the perfect age. So therefore does man receive spiritual life in Baptism, which is a spiritual regeneration: while in Confirmation man arrives at the perfect age, as it were, of the spiritual life. Hence Pope Melchiades says: "The Holy Ghost, Who comes down on the waters of Baptism bearing salvation in His flight, bestows at the font, the fulness of innocence; but in Confirmation He confers an increase of grace. In Baptism we are born again unto life; after Baptism we are strengthened." And therefore it is evident that Confirmation is a special sacrament.
Reply to Objection 1. Concerning the institution of this sacrament there are three opinions. Some (Alexander of Hales, Summa Theol. P. IV, Q. IX; St. Bonaventure, Sent. iv, D, 7) have maintained that this sacrament was instituted neither by Christ, nor by the apostles; but later in the course of time by one of the councils. Others (Pierre de Tarentaise, Sent. iv, D, 7) held that it was instituted by the apostles. But this cannot be admitted; since the institution of a new sacrament belongs to the power of excellence, which belongs to Christ alone.
And therefore we must say that Christ instituted this sacrament not by bestowing, but by promising it, according to John 16:7: "If I go not, the Paraclete will not come to you, but if I go, I will send Him to you." And this was because in this sacrament the fulness of the Holy Ghost is bestowed, which was not to be given before Christ's Resurrection and Ascension; according to John 7:39: "As yet the Spirit was not given, because Jesus was not yet glorified."
Reply to Objection 2. Confirmation is the sacrament of the fulness of grace: wherefore there could be nothing corresponding to it in the Old Law, since "the Law brought nothing to perfection" (Hebrews 7:19).
Reply to Objection 3. As stated above (Question 65, Article 4), all the sacraments are in some way necessary for salvation: but some, so that there is no salvation without them; some as conducing to the perfection of salvation; and thus it is that Confirmation is necessary for salvation: although salvation is possible without it, provided it be not omitted out of contempt.
Reply to Objection 4. Those who receive Confirmation, which is the sacrament of the fulness of grace, are conformed to Christ, inasmuch as from the very first instant of His conception He was "full of grace and truth" (John 1:14). This fulness was made known at His Baptism, when "the Holy Ghost descended in a bodily shape... upon Him" (Luke 3:22). Hence (Luke 4:1) it is written that "Jesus being full of the Holy Ghost, returned from the Jordan." Nor was it fitting to Christ's dignity, that He, Who is the Author of the sacraments, should receive the fulness of grace from a sacrament.
Source: Summa Theologica (New Advent)