Why do you baptize infants?
Why do we baptize infants? Because we believe that the Bible requires it. What you really ask, I surmise, is where in the Bible do we get the authority and the command? It's difficult to know how much of a background understanding you have in the controversy between paedo-baptists and "believer's baptists." So I'll take it step by step.
It would help if there were in Scripture a specific command to baptize new-born children, or to baptize only those old enough to make a credible confession of faith. But God is not obliged to answer such questions the way we want them answered. So we must look both deeper and over a broader expanse of scripture to find the answer.
So we first go back to Genesis 17:7-14. God made a covenant with Abraham and his descendants. It is important to know that that covenant was not with Abraham's physical descendants alone, because in Genesis 12:1-3, when God called Abraham, He made three promises: a land (vs. 1), a nation (vs. 2), and a blessing (vs. 3). In chapter 17, the sign and seal of that three-fold covenant promise was circumcision. Now only male babies can be circumcised. The female infants are also in the covenant because their fathers were circumcised. Abraham was required to be circumcised before Isaac was conceived (Genesis 17:28).
All of the Old Testament ordinances having to do with animal sacrifices for the covenant people of God involved the shedding of blood. All such shedding of blood was done away after the death of Christ, the one and only true Lamb of God. To go on shedding blood after the death of Christ would suggest that His blood is not sufficient. That's why we don't continue the Passover Feast, but have in its place the Lord's Supper. And circumcision calls for the shedding of blood (see Exodus 4:24-26). It is true that Jews and others circumcise their male infants to this day, but after Pentecost it was not required by God (Galatians 6:15)!
But the covenant God made with Abraham is still in force. Genesis 12:3 says, "And in you [Abraham] all the families of the earth shall be blessed." This was a very early prophecy of the spreading of the Gospel over the whole world. Is there a sign to replace circumcision? Yes. The Apostle Paul speaks of it in Colossians 2:11 & 13: "In Him [Christ] you were also circumcised with the circumcision made without hands, by the putting off of the body of the sins of the flesh by the circumcision of Christ." Paul was not talking about literal circumcision, but what circumcision signifies - the new birth through the work of the Holy Spirit (John 3:5). And it was not of Jesus' circumcision when He was eight days old, but the cleansing of our hearts through the blood on Jesus. (vs. 12): "... buried with Him in baptism, in which also you were raised with Him [Christ] through faith in the working of God, who raised Him from the dead." Still speaking of that which circumcision signified - the new birth - Paul brings in baptism as the symbol of Christ's death and resurrection. Read Galatians 2:20 where Paul says that he was crucified with Christ, but he lives by faith in the Son of God who died and rose again. Here Paul is speaking of union with Christ, the state of all true Christians.
Baptism signifies our union with Christ through the New Birth. (vs. 13): "And you, being dead in your trespasses, and the uncircumcision of your flesh [referring to the heart-condition of unbelievers], He [God] has made alive with Him [Christ], having forgiven you all trespasses." It should be clear that through these three verses Paul is talking about the meaning of the new birth, using the language of circumcision in vs. 11, speaking of baptism in vs. 12, and returning to circumcision in vs. 13.
Now neither baptism nor circumcision can save anybody. Circumcision and baptism are performed by man. In John 1:12 & 13 we read, "But as many as received Him [Christ], to them He gave the right to become the children of God, to those who believe in His name: who were born [again], not of blood, nor of the will of the flesh, nor the will of man, but of God." So why do we baptize infants? Because of God's covenant promise.
Perhaps the most telling verse in all Scripture is Acts 2:39: "For the promise [of the Holy Spirit] is to you and your children, and to all who are afar off [the Gentiles], as many as the Lord our God will call." The church on earth includes believers and their children. It's not possible to distinguish between saved and unsaved little children. People must be somewhat grown up before we can be reasonably sure that they are saved through faith in Jesus. But they, like the children of the Old Covenant, are counted as the people of God from birth.
The parents bringing their children for baptism solemnly vow to "instruct their child in the principles of our holy religion as revealed in the Scriptures of the Old and New Testaments, and as summarized in the Confession of Faith and Catechisms of this church; and ... to pray with and for their child, to set an example of piety and godliness before him/her, and endeavor by all the means of God's appointment to bring him/her up in the nurture and admonition of the Lord."
Not all covenant children grow up to turn to the Lord, but many do, as against those reared in non-Christian homes, who seldom turn to Christ. The difference is, as it was in the Old Testament, how faithfully these baptismal vows are kept and whether God, by His Spirit, is pleased to call them to Christ (Acts 2:39, Romans 8:28). New Testament practice seems to indicate that, upon the conversion of parents, both parents and children were baptized (Acts 16:31-33; 1 Corinthians 1:16).
This is a very long answer to such a short question. I hope you will ponder it. And if you have further questions, please feel free to come back with them.
You mentioned that the OPC's Confessions deal with this issue. What part were you referring to? It sounded like the PCA's Book of Church Order.
In answer to your follow-up question concerning the baptism of infants, the Westminster Confession of Faith, Chapter 28 - particularly paragraphs 4 through 6; the Larger Catechism - question 166, and the Shorter Catechism - question 95, have the answer as to the adopted creeds of the OPC. I think you'll find those word-for-word the same as in the PCA. In addition, the OPC Directory for Worship, Chapter 4, paragraphs 1-5, contain the reasoning and the form of administration of covenant baptism. I don't know how closely the PCA form follows that of the OPC, but I would guess that they are similar.
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