Is it legal to terminate parental rights?

During or after a divorce, because one parent is angry that the other won’t let him/her see the kids, or feels that they are paying too much child support, or doesn’t want to pay at all?? Isn’t that parent still liable for child support? If it were legal to terminate, wouldn’t we see more people doing this to “get even” with their spouses?? Well, it’s more than one question, but it’s all tied together, so I hope that it’s okay…I’m not asking about how sick a person would have to be, how they are only hurting their own children, etc., just asking about if it’s legal or not…THANKS!