He took John the Baptist's baptism, not His own.
People who argue for infant baptism refer to circumcision. Yet circumcision was only to mark a promise for a specific people, not a ritual of faith towards God.
People who baptize their babies, and those babies who grow up and stray from God. Those baptisms are in vain. An infant is technically an unbeliever, and there is nothing that supports baptizing unbelievers.
Baptism is the act of dying and being buried with Jesus, then resurrecting into a new person. It's a public deceleration of faith (which an infant can't do). It's an act of obedience (which an infant can't do). It's an agreement with God that you will turn from your old sinful life, and follow Jesus (which an infant can't do).