Let's say I have a right to own a gun. But, let's say that I have no intention of ever owning a gun. Wouldn't it be kind of silly to spend money, time, and effort to give up a right that I never plan to use? It would to me.
So, if the father wants to give up his rights (what he's really saying is that he doesn't want to pay child support - but we'll get to that later), all he has to do is NOT use them. And, that won't cost anybody a penny.
It also seems pretty silly for a mother to spend money, time and effort, to help this guy give up rights he's never going to use. Why would she do that?? If the guy isn't ever going to visit his kids, going to court now isn't going to change that.
However, if this guy wants to give up his rights, that's his RIGHT to do so. Let him spend all the time, money and effort he wants to, to give up a right he never plans to use. Let him be stupid if he wants to be. Of course, he can't give up his OBLIGATIONS.
If it weren't for your kid, I'd say the same thing about you. However, you have another mouth to feed so you can't AFFORD to be stupid. He can give up all the rights he wants, but he CAN'T give up his OBLIGATIONS. In this country, you are OBLIGATED to support your children.
And you, as a new mother, for the sake of your child, should NOT be encouraging him to leave your child fatherless. In addition, you should NOT be encouraging him to leave your child fatherless AND HUNGRY. Besides, it's not YOUR money to refuse. It's your children's money. When they grow up, you'll probably be pissed at them if they throw away YOUR money. Well, I'll be pissed off at you now for throwing away theirs.
PS> I see that this question was asked on behalf of someone else. Ok, just switch the word "you" with "they".