Objection 1. It would seem that this sacrament ought to be given to children. Because children suffer from the same ailments sometimes as adults. Now the same disease requires the same remedy. Therefore this sacrament should be given to children the same as to adults.
Objection 2. Further, this sacrament is given in order to remove the remnants of sin, whether original or actual, as stated above (Question 30, Article 1). Now the remnants of original sin are in children. Therefore this sacrament should be given to them.
On the contrary, This sacrament should be given to none but those to whom the form applies. But the form of this sacrament does not apply to children, since they have not sinned by sight and hearing; as expressed in the form. Therefore this sacrament should not be given to them.
I answer that, This sacrament, like the Eucharist, requires actual devotion in the recipient. Therefore, just as the Eucharist ought not to be given to children, so neither ought this sacrament to be given to them.
Reply to Objection 1. Children's infirmities are not caused by actual sin, as in adults, and this sacrament is given chiefly as a remedy for infirmities that result from sins, being the remnants of sin, as it were.
Reply to Objection 2. This sacrament is not given as a remedy for the remnants of original sin, except in so far as they gather strength, so to speak, from actual sins. Hence from the very form it appears that it is given chiefly as a remedy for actual sins, which are not in children.
Source: Summa Theologica (New Advent)