But a parent cannot refuse citizenship for his minor child, so Obama would still be an American citizen by birth to an American citizen - his mother.
When Barack was born, Stanley Ann was eighteen, not quite old enough to p[ass her citizenship to him ... relative only if he was born on foreign soil, but the British citizenship of his father is relative regardless of where the littel squirrel was born. That divided loyalty is precisely what the framers were seeking to prevent in a POTUS.