I would like to offer a slightly less confusing explanation of why we have a natural born citizen requirement.
It is not where one is born, but where his allegiances may lie. The NBC requires both parents to be U.S. citizens at the time of a child’s birth. A president, who is commander in chief of the U.S. military, cannot have any questionable allegiances through the nationality of one of his parents.
Most legal disputes have the incorrect evidence of WHERE one is born, rather than WHO the parents are.