He does not relinquish his legal rights unless the child is adopted (or the Department of Social Services files for termination). If he does not want to be a father, then I assume he does not interfere with you raising the child, so why would you need to be able to terminate his rights? One day, he might straighten himself out and actually be able to be a good parent. Until then, he should at least be paying child support.
This response does not create an attorney-client relationship and is intended for general information purposes only.