The practice of infant baptism since the time of the early church was part of Augustine’s argument for original sin: it was clear that infants did not sin; they have inherited sin, otherwise baptism would be irrelevant.
Baptism is a sacrament, which Augustine defined as ‘an outward and visible sign of an inward and invisible grace.’ Baptismal water is used by God to save.
Augustine said that infant baptism is like the removal of a disease; one is left in a weakened condition; this weakness is remedied by Christian growth and other sacraments.
Zwingli supported infant baptism on the grounds that it replaced circumcision as a sign of the covenant (Colossians 2:11-12), Christ welcomed children (Matthew 9:13-14), and that it is an occasion for parents to make pledges.
20th century theologian Karl Barth supported ‘believer’s baptism’: baptism only following a profession of faith – usually by full immersion (Acts 8:35-36).
Barth stressed that it is the person of Jesus is the sacrament of God (the outward sign of an inward and invisible grace) – not any ritual of the church.
Churches that practice infant baptism require promises from parents and others to raise the child in the faith until they ‘confirm’ their faith as adults.