The 14th Amendment says:
“All persons born or naturalized in the United States, and subject to the jurisdiction thereof, are citizens of the United States and of the State wherein they reside. No State shall make or enforce any law which shall abridge the privileges or immunities of citizens of the United States; nor shall any State deprive any person of life, liberty, or property, without due process of law; nor deny to any person within its jurisdiction the equal protection of the laws.”
Ms Haley was born in the United States, so she is a citizen. But you are saying that a citizen of the United States cannot run for President? You are unequivocally incorrect.
And by this sophistry, citizenship ceases to have any meaning.
The 14 amendment makes you a citizen but it doesn’t make you a natural born citizen