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Some Christians baptize infants. They think that what we see in Acts 2, this promise is to you and your children… they think that that means that the promises of God go down the generations, and, therefore, if believers have children, those children have the right to the sign of the covenant, like the children of the Israelites did in the Old Testament with the sign of circumcision.
I'm not persuaded that's a good way to understand Acts 2:38, or the whole way the New Testament talks about baptism. Peter does say there to those that are far off as well, and yet we don't go baptizing those who are far off because we're baptized.
I want to be careful in talking about this because there are brothers and sisters whom I love in the Lord and respect, and learn from all the time who really understand Scripture differently on this point than I do. But I'm convinced that, no, infants should not be baptized. Baptism is for believers. Baptism reflects the newness of life that God has given to us in Christ. It's a picture of the new birth, and a picture of our hope in the resurrection of the body to come.
So I think that even as most of my friends who believe in infant baptism would only admit believers to the Lord's table, and that doesn't undermine the fact that it's a gracious ordinance, a gracious sacrament just by the fact that we participate in it. It doesn't undermine the graciousness of God's promises held out to us in Christ in baptism for us to require faith. Our faith. That faith is a gift, as we know from Ephesians 2. But it doesn't undermine the graciousness of it to say, well, it is by faith that we're saved, and therefore, those who are baptized, we know from Romans 6, looks like there are those that have participated in this new in life in Christ by faith. So those are the people, according to the Bible, who should be baptized, and not infants.