Objection 1. It would seem that it was unbecoming when Christ was baptized for the Father's voice to be heard bearing witness to the Son. For the Son and the Holy Ghost, according as they have appeared visibly, are said to have been visibly sent. But it does not become the Father to be sent, as Augustine makes it clear (De Trin. ii). Neither, therefore, (does it become Him) to appear.
Objection 2. Further, the voice gives expression to the word conceived in the heart. But the Father is not the Word. Therefore He is unfittingly manifested by a voice.
Objection 3. Further, the Man-Christ did not begin to be Son of God at His baptism, as some heretics have stated: but He was the Son of God from the beginning of His conception. Therefore the Father's voice should have proclaimed Christ's Godhead at His nativity rather than at His baptism.
On the contrary, It is written (Matthew 3:17): "Behold a voice from heaven, saying: This is My beloved Son in whom I am well pleased."
I answer that, As stated above (Article 5), that which is accomplished in our baptism should be manifested in Christ's baptism, which was the exemplar of ours. Now the baptism which the faithful receive is hallowed by the invocation and the power of the Trinity; according to Matthew 28:19: "Go ye and teach all nations, baptizing them in the name of the Father, and of the Son, and of the Holy Ghost." Wherefore, as Jerome says on Matthew 3:16-17: "The mystery of the Trinity is shown forth in Christ's baptism. our Lord Himself is baptized in His human nature; the Holy Ghost descended in the shape of a dove: the Father's voice is heard bearing witness to the Son." Therefore it was becoming that in that baptism the Father should be manifested by a voice.
Reply to Objection 1. The visible mission adds something to the apparition, to wit, the authority of the sender. Therefore the Son and the Holy Ghost who are from another, are said not only to appear, but also to be sent visibly. But the Father, who is not from another, can appear indeed, but cannot be sent visibly.
Reply to Objection 2. The Father is manifested by the voice, only as producing the voice or speaking by it. And since it is proper to the Father to produce the Word--that is, to utter or to speak--therefore was it most becoming that the Father should be manifested by a voice, because the voice designates the word. Wherefore the very voice to which the Father gave utterance bore witness to the Sonship of the Word. And just as the form of the dove, in which the Holy Ghost was made manifest, is not the Nature of the Holy Ghost, nor is the form of man in which the Son Himself was manifested, the very Nature of the Son of God, so neither does the voice belong to the Nature of the Word or of the Father who spoke. Hence (John 5:37) our Lord says: "Neither have you heard His," i.e. the Father's, "voice at any time, nor seen His shape." By which words, as Chrysostom says (Hom. xl in Joan.), "He gradually leads them to the knowledge of the philosophical truth, and shows them that God has neither voice nor shape, but is above all such forms and utterances." And just as the whole Trinity made both the dove and the human nature assumed by Christ, so also they formed the voice: yet the Father alone as speaking is manifested by the voice, just as the Son alone assumed human nature, and the Holy Ghost alone is manifested in the dove, as Augustine [Fulgentius, De Fide ad Petrum] makes evident.
Reply to Objection 3. It was becoming that Christ's Godhead should not be proclaimed to all in His nativity, but rather that It should be hidden while He was subject to the defects of infancy. But when He attained to the perfect age, when the time came for Him to teach, to work miracles, and to draw men to Himself then did it behoove His Godhead to be attested from on high by the Father's testimony, so that His teaching might become the more credible. Hence He says (John 5:37): "The Father Himself who sent Me, hath given testimony of Me." And specially at the time of baptism, by which men are born again into adopted sons of God; since God's sons by adoption are made to be like unto His natural Son, according to Romans 8:29: "Whom He foreknew, He also predestinated to be made conformable to the image of His Son." Hence Hilary says (Super Matth. ii) that when Jesus was baptized, the Holy Ghost descended on Him, and the Father's voice was heard saying: "'This is My beloved Son,' that we might know, from what was accomplished in Christ, that after being washed in the waters of baptism the Holy Ghost comes down upon us from on high, and that the Father's voice declares us to have become the adopted sons of God."
Source: Summa Theologica (New Advent)