The Catholic Encyclopedia relates that the following statements are anathematized by the Council of Trent:
Infants, not being able to make an act of faith, are not to be reckoned among the faithful after their baptism, and therefore when they come to the age of discretion they are to be rebaptized;
or it is better to omit their baptism entirely than to baptize them as believing on the sole faith of the Church, when they themselves can not make a proper act of faith.
Those baptized as infants are to be asked when they have grown up, whether they wish to ratify what their sponsors had promised for them at their baptism, and if they reply that they do not wish to do so, they are to be left to their own will in the matter and not to be forced by penalties to lead a Christian life, except to be deprived of the reception of the Eucharist and of the other sacraments, until they reform.
These certainly are extreme, but they are not without sense.
Israelites circumcised their children as a sign of their incorporation into the people of God. Thus, Jesus is said to be born “under the Law,” i.e., as a proper Jew with all the legal requirements of His birthright fulfilled, with no questionable hanky-panky whatsoever. Christian baptism signifies something similar: a person becomes a member of the Catholic Church and joins the body of Christ. He is lawfully a Christian.
But look, an infant cannot attend mass; he does not know what the meaning of the word “God” is; he cannot receive grace, because the Holy Spirit has nothing to work with.
So, I’d say, an infant is baptized, while for his own sake, but not directly. The party signifying is his parents who are thereby obligated to raise the child as a Christian. The parents can’t just be “open-minded” and hands-off with the kid, expecting him to grow up and then at the age of 14 peruse his choices and wisely pick a religion, if any, for himself to adhere to.
This becomes especially plausible, if we reflect that for every other sacrament, including adult baptism (and indeed marriage), the person undergoing it is making the sign himself. Only for infant baptism is the sign for the child made by someone else. Well, you sign the contract, you fulfill it, in this case by doing your job as a parent.
The Church, recognizing the circuitous way in which (I think) infant baptism works, provides a sure remedy: the sacrament of confirmation. For example, when I became a Catholic at the age of 27, both baptism and confirmation were administered to me and my RCIA fellows in one ceremony. Which kind of shows they they serve a similar purpose. It’s true, as St. Thomas writes, that “confirmation is to baptism as growth to birth. Now it is clear that no one can be brought to perfect age unless he be first born: and in like manner, unless a man be first baptized, he cannot receive the sacrament of confirmation.” (III, 72, 6) But there is little reason to be born, unless one reaches the age of reason; hence confirmation is an essential sacrament, unlike, say, holy orders which need not be taken. It’s a natural (or supernatural, as the case may be) rite of passage.
In addition, however, in the present liberal (in a good sense) world with churches properly separated from the state, one really can’t be forced to practice a religion without his consent. So, I think the Church really kind of has to ask a young person who was baptized as an infant as a matter of policy: Look, are you now a believer? I think therefore that in principle a Catholic shouldn’t even be allowed to receive other sacraments if he refuses to be confirmed, though how strictly this should be enforced cannot be settled a priori.