A friend asks for the basic argument for infant baptism, and how it relates to circumcision, and John the Baptist's and Jesus' baptisms.
In the Old Testament God used circumcision as the sign and seal of including children in his covenant with their believing parents (Genesis 17). In the New Testament the covenant is the same, children are still involved in covenant by implication from 1 Corinthians 7:14-15, but the signs were changed to baptism instead of circumcision. This is clearest in Colossians 2:11-12.
The credo-baptist argument usually sees baptism mainly as our response to God, not so much God's sign sovereignly applied to us. So you wait until our response can be fully intentional and mentally affirmed on the individual's part. The infant baptist position sees it more continuous with the OT, when God did NOT wait for our response and specifically set the sign of the covenant on us 8 days after birth. God loved and included us in Him first, by grace. We love Him because He loved us.
The Reformed churches historically developed the practice of profession of faith to deal with the expected issue of children who grow up in the faith, are baptized in infancy, and who make an individual commitment to Christ at some point. In the NT this response only involves baptism for those hearing the gospel for the first time, NOT for children who grew up in the faith. The Bible nowhere directly addresses what to do sacramentally with children of believers, except in Genesis 17. Israel developed the practice of having children of 12 go to Passover for a special occasion, which became barmitzvah, when they owned their faith themselves. It's good to have some practice like that, that acknowledges a child's own new commitment. But the Bible does NOT raise that to the level of a sacrament. "Repent and be baptized" is for first converts. The pattern in Genesis 17:10-14 is for their children.
Your understanding of the covenant and who is in the church is also involved. The more baptistic understanding is, you're either saved or not, that's it. If you express faith you are counted among the number; if not, then not. The Reformed view adds what we find in the Bible, the "dimension" of covenant. All those circumcised in the OT (Israelites 8 days old and up, and some Gentile converts) are part of Israel, whether they have expressed faith or not. They are in God's covenant. The sign of that covenant is circumcision, or baptism now. So all adult converts to Christ and the children of believers should be baptized and counted part of the church (thus invited to the Lord's Table).
Circumcision isn't explained in the NT, because it assumes you know the OT.
Yes, John was probably an Essene. Even if not, baptism was always a general sign of accepting entrance into something. John uses it to prepare Israel for her Messiah, as an expression that even Israel needs to repent and be saved by Him. John calls Israel to enter a state of preparedness for Messiah by showing your humble and repentant heart.
After Jesus, baptism becomes a sign of the covenant. In Matt 28:18-20 Jesus attaches it to making converts and disciples for Him, and makes it in the Triune name of God. Romans 6 makes its essential meaning that of union with Christ. Colossians 2 shows it replaces circumcision in function, so we retain the circumcision pattern of when we apply the sign (in infancy).
As far as Jesus' baptism by John, Jesus says it is to fulfill all righteousness. This is usually understood to mean that as Jesus begins His ministry, He identifies with His people, who need to be baptized. Jesus didn't need to be baptized just like He didn't need to become a man and save us. But He did became like us to save us, and baptism is part of that package. Israel wandered 40 years in the desert, then crossed the Jordan into Canaan to receive the promised land. Jesus fasted in the desert 40 days, then is baptized in the Jordan to bring us salvation.