Objection 1. It would seem that Christ was baptized at an unfitting time. For Christ was baptized in order that He might lead others to baptism by His example. But it is commendable that the faithful of Christ should be baptized, not merely before their thirtieth year, but even in infancy. Therefore it seems that Christ should not have been baptized at the age of thirty.
Objection 2. Further, we do not read that Christ taught or worked miracles before being baptized. But it would have been more profitable to the world if He had taught for a longer time, beginning at the age of twenty, or even before. Therefore it seems that Christ, who came for man's profit, should have been baptized before His thirtieth year.
Objection 3. Further, the sign of wisdom infused by God should have been especially manifest in Christ. But in the case of Daniel this was manifested at the time of his boyhood; according to Daniel 13:45: "The Lord raised up the holy spirit of a young boy, whose name was Daniel." Much more, therefore, should Christ have been baptized or have taught in His boyhood.
Objection 4. Further, John's baptism was ordered to that of Christ as to its end. But "the end is first in intention and last in execution." Therefore He should have been baptized by John either before all the others, or after them.
On the contrary, It is written (Luke 3:21): "It came to pass, when all the people were baptized, that Jesus also being baptized, and praying;" and further on (Luke 3:23): "And Jesus Himself was beginning about the age of thirty years."
I answer that, Christ was fittingly baptized in His thirtieth year. First, because Christ was baptized as though for the reason that He was about forthwith to begin to teach and preach: for which purpose perfect age is required, such as is the age of thirty. Thus we read (Genesis 41:46) that "Joseph was thirty" years old when he undertook the government of Egypt. In like manner we read (2 Samuel 5:4) that "David was thirty years old when he began to reign." Again, Ezechiel began to prophesy in "his thirtieth year," as we read Ezekiel 1:1.
Secondly, because, as Chrysostom says (Hom. x in Matth.), "the law was about to pass away after Christ's baptism: wherefore Christ came to be baptized at this age which admits of all sins; in order that by His observing the law, no one might say that because He Himself could not fulfil it, He did away with it."
Thirdly, because by Christ's being baptized at the perfect age, we are given to understand that baptism brings forth perfect men, according to Ephesians 4:13: "Until we all meet into the unity of faith, and of the knowledge of the Son of God, unto a perfect man, unto the measure of the age of the fulness of Christ." Hence the very property of the number seems to point to this. For thirty is product of three and ten: and by the number three is implied faith in the Trinity, while ten signifies the fulfilment of the commandments of the Law: in which two things the perfection of Christian life consists.
Reply to Objection 1. As Gregory Nazianzen says (Orat. xl), Christ was baptized, not "as though He needed to be cleansed, or as though some peril threatened Him if He delayed to be baptized. But no small danger besets any other man who departs from this life without being clothed with the garment of incorruptibility"--namely, grace. And though it be a good thing to remain clean after baptism, "yet is it still better," as he says, "to be slightly sullied now and then than to be altogether deprived of grace."
Reply to Objection 2. The profit which accrues to men from Christ is chiefly through faith and humility: to both of which He conduced by beginning to teach not in His boyhood or youth, but at the perfect age. To faith, because in this manner His human nature is shown to be real, by its making bodily progress with the advance of time; and lest this progress should be deemed imaginary, He did not wish to show His wisdom and power before His body had reached the perfect age: to humility, lest anyone should presume to govern or teach others before attaining to perfect age.
Reply to Objection 3. Christ was set before men as an example to all. Wherefore it behooved that to be shown forth in Him, which is becoming to all according to the common law--namely, that He should teach after reaching the perfect age. But, as Gregory Nazianzen says (Orat. xxxix), that which seldom occurs is not the law of the Church; as "neither does one swallow make the spring." For by special dispensation, in accordance with the ruling of Divine wisdom, it has been granted to some, contrary to the common law, to exercise the functions of governing or teaching, such as Solomon, Daniel, and Jeremias.
Reply to Objection 4. It was not fitting that Christ should be baptized by John either before or after all others. Because, as Chrysostom says (Hom. iv in Matth. [From the supposititious Opus Imperfectum), for this was Christ baptized, "that He might confirm the preaching and the baptism of John, and that John might bear witness to Him." Now, men would not have had faith in John's testimony except after many had been baptized by him. Consequently it was not fitting that John should baptize Him before baptizing anyone else. In like manner, neither was it fitting that he should baptize Him last. For as he (Chrysostom) says in the same passage: "As the light of the sun does not wait for the setting of the morning star, but comes forth while the latter is still above the horizon, and by its brilliance dims its shining: so Christ did not wait till John had run his course, but appeared while he was yet teaching and baptizing."
Source: Summa Theologica (New Advent)