Objection 1. It seems that children should not be baptized. For the intention to receive the sacrament is required in one who is being baptized, as stated above (Article 7). But children cannot have such an intention, since they have not the use of free-will. Therefore it seems that they cannot receive the sacrament of Baptism.
Objection 2. Further, Baptism is the sacrament of faith, as stated above (39, 5; 66, 1, ad 1). But children have not faith, which demands an act of the will on the part of the believer, as Augustine says (Super Joan. xxvi). Nor can it be said that their salvation is implied in the faith of their parents; since the latter are sometimes unbelievers, and their unbelief would conduce rather to the damnation of their children. Therefore it seems that children cannot be baptized.
Objection 3. Further, it is written (1 Peter 3:21) that "Baptism saveth" men; "not the putting away of the filth of the flesh, but the examination of a good conscience towards God." But children have no conscience, either good or bad, since they have not the use of reason: nor can they be fittingly examined, since they understand not. Therefore children should not be baptized.
On the contrary, Dionysius says (Eccl. Hier. iii): "Our heavenly guides," i.e. the Apostles, "approved of infants being admitted to Baptism."
I answer that, As the Apostle says (Romans 5:17), "if by one man's offense death reigned through one," namely Adam, "much more they who receive abundance of grace, and of the gift, and of justice, shall reign in life through one, Jesus Christ." Now children contract original sin from the sin of Adam; which is made clear by the fact that they are under the ban of death, which "passed upon all" on account of the sin of the first man, as the Apostle says in the same passage (Romans 5:12). Much more, therefore, can children receive grace through Christ, so as to reign in eternal life. But our Lord Himself said (John 3:5): "Unless a man be born again of water and the Holy Ghost, he cannot enter into the kingdom of God." Consequently it became necessary to baptize children, that, as in birth they incurred damnation through Adam so in a second birth they might obtain salvation through Christ. Moreover it was fitting that children should receive Baptism, in order that being reared from childhood in things pertaining to the Christian mode of life, they may the more easily persevere therein; according to Proverbs 22:5: "A young man according to his way, even when he is old, he will not depart from it." This reason is also given by Dionysius (Eccl. Hier. iii).
Reply to Objection 1. The spiritual regeneration effected by Baptism is somewhat like carnal birth, in this respect, that as the child while in the mother's womb receives nourishment not independently, but through the nourishment of its mother, so also children before the use of reason, being as it were in the womb of their mother the Church, receive salvation not by their own act, but by the act of the Church. Hence Augustine says (De Pecc. Merit. et Remiss. i): "The Church, our mother, offers her maternal mouth for her children, that they may imbibe the sacred mysteries: for they cannot as yet with their own hearts believe unto justice, nor with their own mouths confess unto salvation... And if they are rightly said to believe, because in a certain fashion they make profession of faith by the words of their sponsors, why should they not also be said to repent, since by the words of those same sponsors they evidence their renunciation of the devil and this world?" For the same reason they can be said to intend, not by their own act of intention, since at times they struggle and cry; but by the act of those who bring them to be baptized.
Reply to Objection 2. As Augustine says, writing to Boniface (Cont. duas Ep. Pelag. i), "in the Church of our Saviour little children believe through others, just as they contracted from others those sins which are remitted in Baptism." Nor is it a hindrance to their salvation if their parents be unbelievers, because, as Augustine says, writing to the same Boniface (Ep. xcviii), "little children are offered that they may receive grace in their souls, not so much from the hands of those that carry them (yet from these too, if they be good and faithful) as from the whole company of the saints and the faithful. For they are rightly considered to be offered by those who are pleased at their being offered, and by whose charity they are united in communion with the Holy Ghost." And the unbelief of their own parents, even if after Baptism these strive to infect them with the worship of demons, hurts not the children. For as Augustine says (Cont. duas Ep. Pelag. i) "when once the child has been begotten by the will of others, he cannot subsequently be held by the bonds of another's sin so long as he consent not with his will, according to" Ezekiel 18:4: "'As the soul of the Father, so also the soul of the son is mine; the soul that sinneth, the same shall die.' Yet he contracted from Adam that which was loosed by the grace of this sacrament, because as yet he was not endowed with a separate existence." But the faith of one, indeed of the whole Church, profits the child through the operation of the Holy Ghost, Who unites the Church together, and communicates the goods of one member to another.
Reply to Objection 3. Just as a child, when he is being baptized, believes not by himself but by others, so is he examined not by himself but through others, and these in answer confess the Church's faith in the child's stead, who is aggregated to this faith by the sacrament of faith. And the child acquires a good conscience in himself, not indeed as to the act, but as to the habit, by sanctifying grace.
Source: Summa Theologica (New Advent)