Actually I think unmarried men should have no rights to children. And unmarried women or their offspring should have no rights to men’s money or support.
The contract of marriage should mean something. Not be whittled away by other laws.
Fatherhood, and the right to be with one’s own family, is a matter of nature.
Unless a parent is unfit, the government has no right to prevent fathers from parenting, for the right to parent was not created by the government in the first place.