My argument doesn't assume that without marriage there will be a father in the picture, that is your assumption, own it.
When any child is born there is ALWAYS a Father in the picture. With SSM the State sanctions and legitimizes a marital relationship that will exclude the Father's involvement as a matter of Social Policy not circumstance. It is BAD SOCIAL POLICY that allows for the creation of a "family" that takes a parent away from a child.
How hard is this to figure out?