Should he have to pay child support if it was a sperm donation - updated

So kinda complicated I’m not going to give any names, but if a single woman wants to be a mother and have a baby on her own so she and this guy made a agreement that he will donate his sperm to her so she can have a baby without paying the cost to go to a sperm bank. The agreement was he will have no part in the baby life and the baby will have no idea who he is. It will be 100% her baby only. It worked and she got pregnant and had the baby. Everything is great she gets what she wants and he did a good deed.

So now she changed her mind and wants him to be a father to the baby. He said no that wasn’t the agreement they had. So now she says she wants child support. They had no legal record of the agreement. So who do you think is right in this situation? And do you think he should now have to pay her child support?

EDIT- It was all verbal agreement nothing written.

EDIT- And I highly doubt his name is on the birth certificate because that was part of the agreement that he has nothing to do with it besides donating sperm. Unless she lied and put his name on it anyway. But that wouldn’t matter because the fathers name doesn’t have to be on the birth certificate for him to pay child support.

Update EDIT - thanks for all the reply’s I left a important piece of information out that might make a difference in the court. They have never had sexual intercourse. They did ejaculation in a cup. Do you think that will make a difference in the court room because technically he didn’t impregnate her she did it herself?