That was their first mistake. Biggest too. Because if Brian, in theory, would have been willing to give up his rights because he said he didn't want a son (which changed after he had Gus, born and alive, in his arms), Michael would have never been so. It was really naive of them to think that. Why should a guy who grew up without a father want his own child to grow up like that too? Plus, Debbie becomes grandmother and has no real rights to her grandchild? No chance in hell
Debibe would have never let Michael give up on his child.