Because nowhere in there is a definition of natural-born citizen.
Given that some argue that NBC is settled, others argue that the meaning is still in flux, and still others argue that the Supreme Court should unequivocally settle this one and for all, consent of the governed has not been established.
That's ridiculous.
There is no definition of "Arms" as in the Second Amendment either, but people of the time period who were not idiots, knew what the term meant without an explicit definition.
As James Madison said:
What could the Convention have done? If they had in general terms declared the Common law to be in force, they would have broken in upon the legal Code of every State in the most material points: they wd. have done more, they would have brought over from G.B. a thousand heterogeneous & antirepublican doctrines, and even the ecclesiastical Hierarchy itself, for that is a part of the Common law. If they had undertaken a discrimination, they must have formed a digest of laws, instead of a Constitution.