Article 2, section 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 eligible to the Office of President; ..."

The only definition of "natural born citizen" that makes sense of this clause's phrasing comes from someone the Founding Fathers were known to have referenced; Vattel.

Vattel's definition of natural born citizen is "a citizen born of citizen parents".

That is, to be President, at the time of your birth your parents must have been citizens of one form or another.

Obama's father was a British subject at the time of his birth. Making him ineligible to hold the office.

The reason Vattel's definition is the correct one is very simple to understand when you know the circumstances of the War of Independence...

King George III was the first British monarch of that name... who spoke English as his first language. He was the head of the Hapsburg dynasty. Y'know... Germans. aka, Not-English.

A century and a quarter later, Queen Victoria's grandson was Kaiser Wilhelm of Germany.

The situation had existed for centuries that the aristocracy of Europe was more loyal to their fellow aristocrats than to the individual countries over which they ruled.

The whole point of clause 5 only makes sense if that point is to ensure there are no mixed loyalties in the White House.