There is some push back on calling him the “birth” father. After all, he didn’t give birth. Often, the father isn’t actually known or is misrepresented by the woman giving birth. I know of situations where these kinds of circumstances exist.
Birth father has commonly be used to refer to a man who’s child is being or has been placed with an adoptive family. The actual man is certainly the genetic father. Some adoptees will derogatively refer to him as their sperm donor and that is accurate too. Others refer to him as their biodad. More than one will say simply that he should be referred to simply as “dad.”
Throughout history, men have had the easy path in human reproduction. Their contribution takes almost no time at all, whereas a woman must devote as much as 9 months of her life for a completely new human being to emerge into the world. Technically, what is referred to as a birth father is one who pays no child support. Often an adoption is finalized without the birth father’s knowledge or consent. If you are not married to the mother of your child at the time of birth, you are considered a ‘putative father,’ meaning reputed to be. Often a genetic father denies he fathered a child until forced to do a paternity test which proves the truth (or not) of the situation.
And realistically this – being called birth father or bio father does not diminish what you as the birth mother have gone through. And this came up repeatedly – it really is up to the child what they chose to call their father. Also, the birth mother who started this was reminded that she needs to be very careful whenever she expresses disagreement because her relationship with her child could be snatched away, at any time – for any reason, that the adoptive parents see fit to do that. Don’t risk it over this because if she gets cut off her child will experience yet another loss. She does not get to be a gatekeeper regarding her child’s relationships. Her issues with her child’s father shouldn’t become her child’s issues. It doesn’t matter when his relationship with his child started because at least he has one now.