It doesn't matter of you're a man or a woman: if you've been ordered to pay child support by the court, you're honor- and legally-bound to do it. Child support law allows the state government to recapture your tax returns and garnish your wages if you don't.
If your child's other parent is ignoring court-ordered child support payments, don't let them get away with it, even if you can manage without them. Report them to the court. Although the system tends to move slowly, child support law requires them to track the culprit down and force payment.