You are correct, but you may see people trying to use Acts 16:15 where it mentions an entire "household" being baptized...they unnecessarily infer that to possibly include young children because young children are common in families.
But obviously that is not a necessary conclusion from the text but just wishful thinking.
I think it also comes from the understanding of what baptism represents. Some churches seem to adopt the theology that it replaces circumcision, which then would make sense that infants are baptised on the faith of their parents. Other churches understand it as a totally new covenant sign (being immersed into Christ with his burial, and then resurrection), which doesn't make sense with infants (as they are unable to believe on Him).
One thing I do understand, but don't like, about infant baptism is that its not really baptism at all. Baptism is supposed to be immersion, and on infants (for good reason), they are sprinkled, rather than immersed. As I understand, Christ is not sprinkled onto us - we are immersed in Him, as per Colossians.
Colossians 2:11 - 17
In whom also ye are circumcised with the circumcision made without hands, in putting off the body of the sins of the flesh by the circumcision of Christ: Buried with him in baptism, wherein also ye are risen with him through the faith of the operation of God, who hath raised him from the dead. And you, being dead in your sins and the uncircumcision of your flesh, hath he quickened together with him, having forgiven you all trespasses; Blotting out the handwriting of ordinances that was against us, which was contrary to us, and took it out of the way, nailing it to his cross; And having spoiled principalities and powers, he made a shew of them openly, triumphing over them in it.
Let no man therefore judge you in meat, or in drink, or in respect of an holyday, or of the new moon, or of the sabbath days: Which are a shadow of things to come; but the body is of Christ.
