"Most men would be mad, but I doubt they would do what he is trying to do and take the kid from the mother."
It would be depressing to know you had a child that you could never meet. I suspect he is just trying to get as much money as he can from the clinic though. To do that he has to establish paternity. The mother ought to call his bluff and demand child support. I bet that would make him change his mind, although, technically the clinic is responsible for the child's creation and so should be legally liable for it's child support. Not the man.
I agree if I found out I fathered a child it would bother me and I would at least like to know if the child is in a stable environment and taken care of, but it would stop there.
I would never seek to get parental rights or try to wedge myself into their family, I would let them know I hope that the child is happy and healthy, and if they ever need any medical information to call me, and that would be it.
I would also ask that if the child finds out and wants to meet me that when they are adults that they give them my address to they can contact me if THEY want, but I would not instigate a meeting at all unless the child knows the truth and wants to meet me themselves.