Protestant
Is infant baptism biblical?
The New Testament describes whole households being baptized, which in ancient family units naturally included infants and children, and Peter says the promise of baptism is 'for you and your children.'
Catholic teaching
Baptism washes away original sin and incorporates the person into Christ's Body by grace, not by the recipient's own act of understanding; since infants share fully in fallen human nature, the Church has always seen fit to bring them to this grace as early as possible.
Biblical foundation
Peter proclaims at Pentecost that the promise of baptism is 'for you and for your children' (Acts 2:38-39), and the book of Acts records the baptism of entire households (Acts 16:15, 16:33), the normal ancient sense of which included children too young to make personal professions.
Scripture references
Historical evidence
Origen in the early third century states that the Church received the practice of baptizing infants 'from the apostles,' and archaeological evidence of infant baptisteries confirms the practice was ancient and widespread, not a later medieval addition.
The Church Fathers
“The Church received from the apostles the tradition of giving baptism even to infants.”