As I have engaged a brother on this issue recently, I would like to put to you, the reader, my basic rationale for why God's Word commands us to baptize the children of a believing parent.
What is baptism? The Westminster Shorter Catechism reminds us that "Baptism is a sacrament, wherein the washing with water in the name of the Father, and of the Son, and of the Holy Ghost, doth signify and seal our ingrafting into Christ, and partaking of the benefits of the covenant of grace, and our engagement to be the Lord's" (#94). References: Acts 2:38-42; Rom. 6:3-4; Gal. 3:26-27, etc.
The key thing to remember is that baptism is a sign and seal of the covenant of grace--a covenant made with Abraham for the salvation of all of God's people through Jesus Christ (Gen. 15). So who should receive this sign and seal? All members of the covenant of grace. Who are members of the covenant of grace?
In Colossians, baptism is closely tied to circumcision, the Old Testament sign and seal of the covenant of grace: "In him also you were circumcised with a circumcision made without hands, by putting off the body of the flesh, by the circumcision of Christ, 12 having been buried with him in baptism, in which you were also raised with him through faith in the powerful working of God, who raised him from the dead" (2:11-12).
So who received circumcision in the Old Testament? Well, Abraham, the recipient of the covenant of grace, for one: "He received the sign of circumcision as a seal of the righteousness that he had by faith while he was still uncircumcised. The purpose was to make him the father of all who believe without being circumcised, so that righteousness would be counted to them as well, and to make him the father of the circumcised who are not merely circumcised but who also walk in the footsteps of the faith that our father Abraham had before he was circumcised" (Rom. 4:11-12).
Abraham received the sign and seal of the covenant of grace because of the righteousness that he had by faith, but that sign and seal was not for Abraham only. In the same passage (Gen. 17), God commanded Abraham to circumcise all men in his household--even Ismael! They were not all believers as Abraham was, but they were members of the covenant of grace by virtue of their relationship to Abraham. As one would expect from a God who manifests his grace through a covenant, He considers those who come into the family of faith or born into the family of faith to be members of the covenant.
Thus, God likewise commanded Abraham to circumcise his son, Isaac, at eight days old (Gen. 21). And this was an abiding command throughout the Old Testament. The children, by virtue of their parent's faith, were considered part of God's covenant of grace. Their bloody circumcision was like a sermon cut into their bodies, reminding them that either they or a substitute would have to be cut off for their sin. The sermon in their flesh cried out for an echo of response--to circumcise their hearts.
Eventually, Christ would Himself be their circumcision, cut off for their sake and ours. But while Christ's fulfillment of the symbolism of circumcision may have changed the form of the sign and seal of the covenant of grace from circumcision to baptism (Matt. 28), He did not change the substance of the sacrament. Baptism was clearly to function as a sign and seal like circumcision, and it's initial use in Acts was tied to the promise made to Abraham (for you and your children after you).
The covenant of grace was fundamentally the same in the New Testament as the Old--sinners were saved by grace through faith in Christ. The key difference was that God's people were no longer looking at a hazy picture of Christ on the horizon, but the historical picture of Christ on the cross--communicated through the preaching of the Word and sacraments.
In the same way, it must be inferred that the signs and seals of the covenant of grace were substantially still the same and the recipients of them still the same. Children were members of the covenant in the Old Testament. Imagine the controversy if such a change had been made! We should expect a command from Christ to do away with something so fundamental. The burden of proof is upon those who would assert that Christ changed the covenant in this way.
But He did not. The command given to Abraham concerning his children abideth still. The numerous household baptisms in Acts can be presumed to be like the household circumcision under Abraham. Again, the burden of proof lies upon those who would contend that the meaning of household with regard to the sacrament had somehow changed between the Old Testament and New, that children would no longer be included in that concept. Rather, Paul tells us in 1 Corinthians 7 that children are sanctified through a believing parent and are considered holy.
Like circumcision, baptism is a sermon written upon the flesh, reminding us that we will one day be submerged by the waters of death for our sin or another in our place. As with circumcision, this act and promise of God cries out for an echo: To embrace by grace and through faith the Christ who was submerged unto death. Every child of a believing parent--rightly considered a member of the covenant of grace--will have that sign and seal of baptism testify to them every day for the rest of their lives.
Paul compares baptism to the Exodus in 1 Corinthians 10. In the Exodus, men, women, and children passed through the waters of death with their mediator, Moses, at their head. The same waters swallowed up the Egyptians. In the same way, parents, send your children through the waters of baptism and regard them as holy (as our Lord does), knowing that such a powerful sermon written upon their flesh will likely reverberate into the echo of saving faith, and if not, will reverberate in their judgment for tasting of the Spirit's continual grace, yet rejecting it.
