If a father gets his girlfriend pregnant, she births the kid, and he ditches his parenting responsibilities without the woman copying him, he is a deadbeat dad and society demands that he pay child support.
If a father gets his girlfriend pregnant, she births the kid, and both parents decide to ditch their parenting responsibilities by setting the kid up for adoption, neither parent is viewed as a deadbeat parent and society thinks this is okay and neither parent has to pay child support.
I'm thinking, it shouldn't matter if your wife decides to abandon her parenting responsibilities and her decision shouldn't impact whether or not you should pay child support. Either you should be legally required to take care of your kids or you shouldn't.
If your legally required to take care of your kids, then adoption would be prohibited as this would be both parents being "deadbeat parents", or it would only be allowed if both parents paid child support. I don't think society wants to force parents who set their kids up for adoption to pay child support.
If your not legally required to take care of your kids, then why are we making deadbeat dads pay child support if they don't have to take care of their kids with child support or a parental presence?