If the born child actually had a right to some particular person's support, it would be criminal to destroy the earnings capabilities of a prospective parent, e.g., by throwing them in jail. Safe haven laws would be all thrown out. It would be a crime to conceal or misrepresent paternity; paternity testing would be mandatory for all born children, as biological paternity is misattributed at a statistically significant rate. All these would be necessary to support a right possessed by a child to have some particular person's support.
Furthermore, transferring that right would require consent of the child, not consent of the parental party, if it were a right held by the child. Adoption of newborns would be impossible under a system which assigned such a right to the child. No; instead, what actually exists is a system which partially couples parental rights and parental obligations. Instead of such a right of the child to support from a particular parent is actually respected by the status quo, what is instead present is the "right" of mothers to assign parental obligation to fathers, willing or not.
I say "right" in scare-quotes because having the "right" to extort money out of someone is generally considered a wrong, and we generally think of "rights" in terms of personal liberties, not personal oppression.






