18 C. Tell me, pray, and rid me of all doubts, why little children are baptized.
A. That their sins may be forgiven them in baptism.
C. What sin are they guilty of? How can any one be set free who is not bound?
A. You ask me! The Gospel trumpet will reply, the teacher of the Gentiles, the golden vessel shining throughout the world: “Death reigned from Adam even unto Moses: even over those who did not sin after the likeness of the transgression of Adam, who is a figure of Him that was to come.” And if you object that some are spoken of who did not sin, you must understand that they did not sin in the same way as Adam did by transgressing God's command in Paradise. But all men are held liable either on account of their ancient forefather Adam, or on their own account. He that is an infant is released in baptism from the chain which bound his father. He who is old enough to have discernment is set free from the chain of his own or another's sin by the blood of Christ. You must not think me a heretic because I take this view, for the blessed martyr Cyprian, whose rival you boast of being in the classification of Scripture proofs, in the epistle addressed to Bishop Fidus on the Baptism of Infants speaks thus: “Moreover, if even the worst offenders, and those who previous to baptism sin much against God, once they believe have the gift of remission of sins, and no one is kept from baptism and from grace, how much more ought not an infant to be kept from baptism seeing that, being only just born, he has committed no sin? He has only, being born according to the flesh among Adam's sons, incurred the taint of ancient death by his first birth. And he is the more easily admitted to remission of sins because of the very fact that not his own sins but those of another are remitted to him. And so, dearest brother, it was our decision in council that no one ought to be kept by us from baptism and from the grace of God, Who is merciful to all, and kind, and good. And whereas this rule ought to be observed and kept with reference to all, bear in mind that it ought so much the more to be observed with regard to infants themselves and those just born, for they have the greater claims on our assistance in order to obtain Divine mercy, because their cries and tears from the very birth are one perpetual prayer.”
Source: Against the Pelagians (New Advent)