Note: It should be noted that a named living person has not claimed guardianship and therefore responsibility over the child.
Sure, if a person in the middle of the wilderness has a kid, then yeah, like any other animal, there's no responsibility over the child.
But in a particular society, there are rules, and they protect the kid for example so that the parents have responsibilities over the child if it is born in that country.
By using the word parent you are implicitly assuming a society. Language is not created in a vacuum. It needs a society.