well from my experience, I'm going to say yes, the guy should have to pay child support. my mom married a complete asshole, and she was with him for ten years (married) and had both me and my brother. he never wanted either one of his children, and he basically ignored us all the time. never worked, never did anything to help. so, my mom divorced him. she had two kids already, she didn't want to take care of a third one. anyway, after she divorced him, he was ordered to pay child support, and he did for a while, but shortly after the checks stopped coming. my mom was too worn down to take him to trial, so she just struggled on as best as she could. so as a result, my mom worked at a dead end job, and could barely afford to make rent and feed me and my brother. so should a guy pay child support? f*** yes.
on the other hand, if the guy marries a complete bitch who divorces him and takes all his money and only spends it on herself, then of course he shouldn't be giving her anything. however, the legal system is screwed up and imperfect, so there's no way to make sure that the money is used for the children.
if the mother in question is single, and young, without a good source of income, I believe that the guy should be forced to pay child support, whether he likes it or not. otherwise it's not fair to the mother or her poor children. on the other hand, if a woman divorces her rich husband, and her children are say teenagers, and she can afford to take care of them herself, then I think it's stupid to make the guy fork over money that won't even be used on the children anyway. that's my opinion