What a fucked up way of looking at things. Jeez.
The court is absolutely fucking the man, and the woman is absolutely greedy in this case.
Your argument hinges on his ability to remedy the situation, but the ability is limited by his knowledge of same. And he did not have knowledge of the situation. He's the victim. The state and the mother are the perpetrator. It's that simple.
Seems like a really simple remedy would be that in the case of any debates over paternity, there should always be a paternity test. Like, if any person goes "this person owes me child support," then the first thing that should be established is a paternity test. That way, you don't end up with a case where the father "doesn't know." Heck, once you get the results, have the court make him sign that he was given the results. Lots of ways to solve ridiculous situations like this.