Objection 1. It would seem that it was not fitting for Christ to be baptized. For to be baptized is to be washed. But it was not fitting for Christ to be washed, since there was no uncleanness in Him. Therefore it seems unfitting for Christ to be baptized.
Objection 2. Further, Christ was circumcised in order to fulfil the law. But baptism was not prescribed by the law. Therefore He should not have been baptized.
Objection 3. Further, the first mover in every genus is unmoved in regard to that movement; thus the heaven, which is the first cause of alteration, is unalterable. But Christ is the first principle of baptism, according to John 1:33: "He upon whom thou shalt see the Spirit descending and remaining upon Him, He it is that baptizeth." Therefore it was unfitting for Christ to be baptized.
On the contrary, It is written (Matthew 3:13) that "Jesus cometh from Galilee to the Jordan, unto John, to be baptized by him."
I answer that, It was fitting for Christ to be baptized. First, because, as Ambrose says on Luke 3:21: "Our Lord was baptized because He wished, not to be cleansed, but to cleanse the waters, that, being purified by the flesh of Christ that knew no sin, they might have the virtue of baptism"; and, as Chrysostom says (Hom. iv in Matth.), "that He might bequeath the sanctified waters to those who were to be baptized afterwards." Secondly, as Chrysostom says (Hom. iv in Matth.), "although Christ was not a sinner, yet did He take a sinful nature and 'the likeness of sinful flesh.' Wherefore, though He needed not baptism for His own sake, yet carnal nature in others had need thereof." And, as Gregory Nazianzen says (Orat. xxxix) "Christ was baptized that He might plunge the old Adam entirely in the water." Thirdly, He wished to be baptized, as Augustine says in a sermon on the Epiphany (cxxxvi), "because He wished to do what He had commanded all to do." And this is what He means by saying: "So it becometh us to fulfil all justice" (Matthew 3:15). For, as Ambrose says (on Luke 3:21), "this is justice, to do first thyself that which thou wishest another to do, and so encourage others by thy example."
Reply to Objection 1. Christ was baptized, not that He might be cleansed, but that He might cleanse, as stated above.
Reply to Objection 2. It was fitting that Christ should not only fulfil what was prescribed by the Old Law, but also begin what appertained to the New Law. Therefore He wished not only to be circumcised, but also to be baptized.
Reply to Objection 3. Christ is the first principle of baptism's spiritual effect. Unto this He was not baptized, but only in water.
Source: Summa Theologica (New Advent)