...By your logic the first situation is Fraud and the second situation is Theft.
And on your second 'statement'.
The father didn't consent to being a father. That's the problem.
Lets be clear.
If the man had prior notification that the woman was pregnant, agreed to be there for her and wanted to be there for the child. THEN leaves, yeah he should pay child support and be able to have rights to the child.
But if the man didn't want anything to do with the kid, doesn't want to be around it and not have any rights to the child and stated this BEFORE she gives birth. Then he shouldn't have to pay child support, because in this instance the woman knows full well, it's going to be on her to raise this kid.
Now if the woman gets pregnant, has the kid, didn't inform the guy, THEN wants to collect on Child Support. That's bullshit because she went without his consent.
Men shouldn't be required to become fathers because of an unwanted pregnancy the same way Women shouldn't be required to become Mothers because of an unwanted pregnancy.