Although many Protestant traditions baptize babies, Baptists—and “Bible churches” in the Baptist tradition—insist that baptism is only for those who have come to faith. Nowhere in the New Testament, they point out, do we read of infants being baptized.
On the other hand, nowhere do we read of children raised in believing households reaching the age of reason and then being baptized. The only explicit baptism accounts in the Bible involve converts from Judaism or paganism. For children of believers there is no explicit mention of baptism—either in infancy or later.
This poses a problem for Baptists and Bible Christians: On what basis do they require children of believers to be baptized at all? Given the silence of the New Testament, why not assume Christian baptism is only for adult converts?
This, of course, would be contrary to historical Christian practice. But so is rejecting infant baptism. As we will see, there is no doubt that the early Church practiced infant baptism; and no Christian objections to this practice were ever voiced until the Reformation.
The New Testament itself, while it does not explicitly say when (or whether) believers should have their children baptized, is not silent on the subject.
Luke 18:15–16 tells us that “they were bringing even infants” to Jesus; and he himself related this to the kingdom of God: “Let the children come to me . . . for to such belongs the kingdom of God.”
When Baptists speak of “bringing someone to Jesus,” they mean leading him to faith. But Jesus says “even infants” can be “brought” to him. Even Baptists don’t claim their practice of “dedicating” babies does this. The fact is, the Bible gives us no way of bringing anyone to Jesus apart from baptism.
Thus Peter declared, “Repent, and be baptized, every one of you, in the name of Jesus Christ for the forgiveness of your sins; and you shall receive the gift of the Holy Spirit. For the promise is to you and to your children” (Acts 2:38–39).
The apostolic Church baptized whole “households” (Acts 16:33; 1 Cor. 1:16), a term encompassing children and infants as well as servants. While these texts do not specifically mention—nor exclude—infants, the very use of the term “households” indicates an understanding of the family as a unit. Even one believing parent in a household makes the children and even the unbelieving spouse “holy” (1 Cor. 7:14).
Does this mean unbelieving spouses should be baptized? Of course not. The kingdom of God is not theirs; they cannot be “brought to Christ” in their unbelief. But infants have no such impediment. The kingdom is theirs, Jesus says, and they should be brought to him; and this means baptism.
Baptism is the Christian equivalent of circumcision, or “the circumcision of Christ”: “In him you were also circumcised with . . . the circumcision of Christ, having been buried with him in baptism and raised with him through your faith in the power of God, who raised him from the dead” (Col. 2:11–12). Thus, like circumcision, baptism can be given to children as well as adults. The difference is that circumcision was powerless to save (Gal. 5:6, 6:15), but “[b]aptism . . . now saves you” (1 Pet. 3:21).
The first explicit evidence of children of believing households being baptized comes from the early Church—where infant baptism was uniformly upheld and regarded as apostolic. In fact, the only reported controversy on the subject was a third-century debate whether or not to delay baptism until the eighth day after birth, like its Old Testament equivalent, circumcision! (See quotation from Cyprian, below; compare Leviticus 12:2–3.)
Consider, too, that Fathers raised in Christian homes (such as Irenaeus) would hardly have upheld infant baptism as apostolic if their own baptisms had been deferred until the age of reason.
For example, infant baptism is assumed in Irenaeus’ writings below (since he affirms both that regeneration happens in baptism, and also that Jesus came so even infants could be regenerated). Since he was born in a Christian home in Smyrna around the year 140, this means he was probably baptized around 140. He was also probably baptized by the bishop of Smyrna at that time—Polycarp, a personal disciple of the apostle John, who had died only a few decades before.
From: http://www.catholic.com/tracts/early-teachings-on-infant-baptism