An explanation of AnswerGuy's answer might help you figure out what to do next:
Generally, the states want children to have TWO parents so that if one can't support the child, the other will have to. They do not want to be providing government assistance to a child whose ABSENT parent could afford it, so they won't let one parent DISOWN a child and avoid responsibility that way.
I assume all you wanted was for him to not have to pay support because YOU were able to support the child (if you were wanting to get government support rather than get teh support from the father, you're out of luck... taxpayers like myself don't love supporting a deadbeat's child and if the father is around, we just don't let that happen just like that)... I assume also that your stbx simply doesn't wnat to have to play daddy.
BOTH of those goals are legitimate and you CAN accomplish them, just without relinquishing parental rights. In the divorce, you give yourself sole custody, give the father the right to move out of town and zero visitation time until he chooses to get counseling (it gives him the option to change his mind at a later date once he's had the chance to get away from the divorce trauma), and you waive child support, showing to the judge that you are fully capable of supporting yourself and the child on your own without his or government support.
And then if another man comes into the picture and wants to be the fahter, you can terminate parental rights at the same time as you petition for step-parent adoption.
NOW, if you were wanting to terminate his rights because you didn't want to deal with him about support, he wants to become a deadbeat, and you wnated to be eligivle to receive government assistance because your child is officially fatherless, it won't happen. Prepare yourself for whatever you have to, for the battle to get support from your ex, understanding that if you DO end up getting government support because he becomes a deadbeat, then the government will probably chase him down and want to put him in jail over it eventually, even if you'd rather just forget about it all.