Why release parental rights of child?

if a non custodial parent releases the right to the child then they dont have to pay the custodial parent any child support.. and the other person can let the child be adopted if they get remarried... it usally comes down to the person releasing the right of a child so they dont have to pay any support.. my ex wanted to do that when our daugher did not want to see him.. but i was able to talk her into giving him another chance..see they were so different in personality they have a hard time to get along.. but i still think that she need her father in her life