Children have the same right to be supported by both parents. There are no distinctions because from the point of view of the child, he/she is not the one responsible for existing.
Segregating children by something that is beyond their responsibility is how we get to the point of some children being deemed having a right to live and some not.
We’re back full circle to making the child pay the price for the one or both parents abdicating personal responsibility.
Apparently, that is still all that matters (that adults get the option to abdicate responsibility). This is exactly how we arrived at the culture of abortion in the first place.
My point is that, by removing downsides to having kids out of wedlock (ie, the girl could get the guy to pay child support with or without marriage), it directly and predictably led to a large increase in out-of-wedlock births.