[[If I am is paris with the wife and she has our kid, how does that preclude them in any way from being American?]]
Exactly- what matters is that the parents have declared their citizenship and that is what determines their child’s citizenship UNTIL the child is old enough to move away and gain their own citizenship in another country-
Thee is citizenship and there is that special class, natural born citizen. Both are citizens but one must meet a higher standard.
Not typing right: Thee = There.