Baptismal Regeneration isn’t a term you’ll find in the Bible. It is a made up term used as a “straw man” argument by those who deny the necessity of baptism for salvation. A “straw man” argument is a tactic used by those who can’t answer an opposing view directly so they create a “straw man” and attack that instead. Then, showing the fake argument to be incorrect, they will assert that they have disproved the actual point when they really haven’t even touched it. By saying that the view of baptismal regeneration is false, those that deny the true biblical teaching on baptism claim they have proved their point. Actually what they’ve done is disprove something that no one agrees with or is even teaching in the first place.
“Baptismal regeneration” is the idea that baptism itself is what saves a person. That is, the act – in and of itself – of being baptized saves a person. Such an idea is, indeed, unscriptural and not at all what the Bible teaches about baptism. There is nothing “magical” or inherently powerful about the water of baptism that washes away a person’s sins. The water is just water! The saving power is in Christ and the gospel (Romans 1:16). The Bible doesn’t say to have faith in the water. It says to have faith in the working of God (Colossians 2:12).
Paul said “you were … buried with Him in baptism, in which you also were raised with Him through faith in the working of God, who raised Him from the dead.” So, the new birth that takes place in baptism is the result of “faith in the working of God.” The word “faith” here means, “to believe to the extent of complete trust and reliance” (Louw & Nida, vol. 1, p. 375).
A person obeys the gospel by joining with Christ in His death, burial, and resurrection (Romans 6:3, 4). This is done by being baptized “into His death” as a repentant believer (Mark 16:16). It is that “obedience to the faith” (Romans 1:5; 16:26), that puts one into Christ (Galatians 3:26, 27) and brings about the new life in Him (Colossians 2:12). It is a person’s “complete trust and reliance” in God that saves them. It is not the water! It is the obedience of faith that brings salvation in Christ.
About the closest you will come to the term “baptismal regeneration” in the Bible is in Titus 3:5, “the washing of regeneration and renewing of the Holy Spirit.” Regeneration here means, “to experience a complete change in one’s way of life to what it should be, with the implication of return to a former state or relation—‘to be born again, to experience new birth, rebirth’” (Louw & Nida, vol. 1, p. 509). There is no question that Paul taught that the new birth occurs at the point of baptism but that’s not what people mean when they say “baptismal regeneration.”