Article II sec. 1 clause 5
No Person except a natural born Citizen, or a Citizen of the United States, at the time of the Adoption of this Constitution, shall be ...
The purpose of the exclusion for themselves (or a citizen at the time) was because they knew it would take 35 years to produce the first eligible natural born citizen of this new country.
One is only naturally a citizen when one cannot be anything else by being born here of citizen parents.
When one is born of foreign nationals, one inherits foreign nationalities, allegiances and loyalties and is not naturally an American.
Thanks Justice Kennedy.