What are the pros and cons of agreeing with him and letting. Him terminate. His rights and how is it done

He can only terminate his rights if the child is being placed for adoption with a new couple, or another man is asking to adopt the child. Other than that, he can't terminate his rights.

First, you are laboring under a inaccurate assumption that he can voluntarily give up his rights. There is a myth that a parent can just give up their rights, but its only a myth.

So, since he can't give up his rights, there are no pros and cons to discuss. Do you want to explain more about this situation? Are/were you married? Is he a part of the child's life? Does he pay child support?

Assuming you are in US, or Canada, he can not give up his rights, it is just not done. They can be taken but the rules for that vary by location.

So there is no discussion, since it is just not possible