I don't think it is quite possible unless the dad gives up his parental rights (as long as the mother request it but it would mean she will have to raise her child on a single income so rarely any mother would do that because they want the best for their child) . The child should be mad at the dad for giving up his parental rights. I have two relatives relating to this. One of them gave up parental right to the grandma (after the mother died) and now his son did not want to have anything to do with his father.
The other adopted a son through marriage which he signed to be his father.. and the father had to be willing to give up his parental rights to him... and he did. he was free from child support. The adopted father is responsible for child support but he was willing to take that responsibility because the real father neglect his son anyhow. If I was going to be mad, I would be mad at anyone who gave up his parental rights.
Up until a few years ago, men who had adulterous wives who got pregnant due to the affair, were required to pay child support for the child that was not even biologically theirs.
The reason being, is because if a child is born during a marriage, it is legally the child of the married husband and wife. The biological father has no rights period.
Now ... men have the right to divorce and take the child away from both biological parents - the cheating wife and the biological father - or, divorce and not pay any support.
Before the law was changed, the husband had to pay child support regardless (usually ended up in a divorce and ex husband was paying for his wife to continue the relationship she had started when she cheated). Now, the husband can "opt out" of situations like that.
Usually, but not always, when I see situations where an adoptive "step-dad" comes in, the relationship started between a cheating wife and the "step-dad" while the biological father had absolutely no idea. The "step-dad" and the cheating wife then conspire to have the children taken from the biological father.
This happens more often than people may realize. I may know the exact same person you are referring to, and I may know the exact reasons why that happened
You never know.