A friend recently asked me, "Why do Presbyterians baptize babies?" Here's my answer:
As a credobaptist, I believe that, biblically, baptism is reserved for believers alone. I also believe that immersion is, by definition, the only form of baptism. So, strictly speaking, I don't believe that Presbyterians (or other paedobaptists) baptize infants at all. They sprinkle them, and since baptism simply is immersion (that's what the word means) paedobaptists don't actually baptize their children.
Let's set the form of baptism aside, though, because the question is really about the proper subjects of baptism (who should be baptized) rather than the form of baptism (how they should be baptized). Although the reasons for "baptizing" infants differ, it seems that, once one weeds out those groups who believe in baptismal regeneration (they sprinkle infants because they believe baptism is salvific), there is basically only one reason to baptize infants: baptism has replaced circumcision as the outward sign marking one's entrance into the covenant community. Beginning with the Abrahamic covenant, the sign of entrance into God's covenant people was circumcision, however, with the inauguration of the new covenant, circumcision has been replaced by baptism. On this point, I am in agreement with the paedobaptist. The problem, however, is that infants are not part of the New Covenant.
Presbyterians (and other Reformed paedobaptists) will argue, though, that infants (the children of believers) are in the New Covenant. This is based on their belief that all the major covenants in Scripture (from Abraham onward) are actually different administrations of one and the same covenant. The argument goes like this, "The Abrahamic covenant included the children of believers, so too, then, must the New Covenant, for it is actually a renewal and fuller revelation of God's previous covenant started with Abraham."
Covenantal credobaptists contend that our paedobaptist brothers have gotten it wrong by overplaying the continuity between the covenants (to the point that they believe that these multiple covenants are actually different administrations of one covenant). Yes, there is one way of salvation progressively revealed though one, unified covenantal plan, but, it does not follow that there are no real differences between the covenants. The New Covenant really is a new covenant. The Abrahamic covenant is not identical with the New Covenant; instead, it prefigures the New Covenant. God's covenant with Abraham is one of promise while the New Covenant is one of fulfillment. Because the pinnacle of redemptive revelation in found in the New Covenant, one must interpret the types and shadows of the Old Testament covenants in light of the New rather than reading the Old into the New.
And what is it that makes this New Covenant so new? The newness of the New Covenant is found in the fact that it is efficacious, meaning that everyone in it is actually saved (Jeremiah 31:33-34). Its membership consists, then, of believers alone rather than believers and their children (who may or may not believe). It is entered, not by birth, but by new birth (John 3:5-8). The visible covenant community—the local church—should, as much as possible, reflect the actual covenant community—the universal church consisting of all the elect (1 Corinthians 5:12-13; 2 Corinthians 6:14-15). The church should consist only of those who actually claim to be believers—those who profess faith (something infants are unable to do).
This is not to say that infants can't actually possess faith. God is free to save his people when and how he pleases, and there seems to be a precedent in Scripture for God saving individuals even before they leave their mother's womb (Luke 1:15, 40-41). This doesn't change the fact that baptism is for professing believers only. Baptism is symbolic rather that salvific, corresponding to entrance into the visible covenant community rather than the actual covenant community. This means that, in theory, one could be saved (and therefore a member of the New Covenant) without being a member of the visible covenant community (i.e. a baptized member of a local congregation). It's not hard, after all, to find examples of adult believers who are born again for some time before being baptized and admitted into church membership. There is no problem, then, for reserving baptism for professing believers even while recognizing that there may be believers who cannot profess faith.