Well, child support doesn't work like a contract between parties. It's a legal obligation, like income tax and GST, so even if he did say not to pay it, you'd still have to pay it, and likewise, even if he did nothing to pursue the debt earlier, that doesn't mean the debt goes away. The only real exception is if you and he had entered into a binding financial agreement that said otherwise.
I'm not trying to strike the fear into you, more just give you a realistic expectation around the situation, that's all.