You evade the distinction between “citizen” and “natural born citizen.”
Not at all. The term "natural born citizen" is not defined in the Constitution. So instead, you are just using your own idiosyncratic definition of the term while ignoring the plain text of the 14th Amendment. So as a reminder, here it is:
Section 1. 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.
By it's own terms, the amendment says that if you are born in the United States, you are a citizen at birth. That was not the law at the time the Constitution was ratified, but that changed with the passage of the 14th Amendment. Such individuals who are "born" in this country are different from people who are naturalized, and the 14th makes that clear as well.
So the 14th described two specific classes of citizens: Those who are citizens at birth, and those who are naturalized. By the plain meaning of the language, a person who is born a citizen is a "natural born citizen", and therefore is eligible to be President. But a person who is only naturalized, like Scharzenegger and other immigrants, is not a "natural born citizen", and therefore ineligible to be President.
But instead, you want to take the undefined phrase "natural-born citizen", and interpret it to exclude people who were born as citizens. That is simply nonsensical. Whatever meaning you might have assigned that phrase in 1787, the plain text of the 14th Amendment changed that. To the extent you're arguing that someone born a citizen is not a "natural born citizen" (as opposed to a naturalized citizen), you're arguing from a liberal, activist position of trying to ignore the plain, common sense meaning of the language.
Now if you want to argue that Obama wasn't even born in this country, fine. But arguing that he isn't a natural born citizen even if he was born in this country runs directly afoul of the plain text of the 14th Amendment.