Why do we baptize babies?

One of the strongest proofs for why we baptize the children of believers is because of the continuity of the Old and New Testament. Baptism of the New Testament is the continuation of Old Testament circumcision (which was administered to children of the Covenant Community). Below is a helpful chart which gives some of the parallels.

Act 16:32-34 And they spoke the word of the Lord to him and to all who were in his house. (33) And he took them the same hour of the night and washed their wounds; and he was baptized at once, he and all his family. (34) Then he brought them up into his house and set food before them. And he rejoiced along with his entire household that he had believed in God.

(Act 16:15)
And after she was baptized, and her household as well, she urged us, saying, "If you have judged me to be faithful to the Lord, come to my house and stay." And she prevailed upon us.

(1Co 1:16)
(I did baptize also the household of Stephanas. Beyond that, I do not know whether I baptized anyone else.)

Circumcision

Baptism

Col 2:11In him you were also circumcised, in the putting off of the sinful nature,[a] not with a circumcision done by the hands of men but with the circumcision done by Christ, Represents: Cutting away of Sin & inclusion into the people of God (Israel) & a life dedicated to God Circumcision done by Christ: is Circumcision of the heart by the Holy Spirit; which transforms our heart Romans 2:29No, a man is a Jew if he is one inwardly; and circumcision is circumcision of the heart, by the Spirit, not by the written code.

Col2:12having been buried with him in baptism and raised with him through your faith in the power of God, who raised him from the dead. Represents: Washing away of sin and inclusion into the people of God (the Church) & a life dedicated to God Baptism done by Christ: Baptism of the Holy Spirit by the Holy Spirit, which transforms our hearts. Mark1:8 I baptize you with[ a] water, but he will baptize you with the Holy Spirit."