Because 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." some people mistakenly interpret that to mean that the only way to be a US citizen is to either be born in the US or to be naturalized in the US. They then go on to surmise that since McCain was not born in the US, he must therefore be a naturalized citizen. That is an incorrect use of phraseology.

What it's saying is that if a person is born or naturalized in the United States, and subject to the jurisdiction thereof, then they have a Constitutional right to US citizenship. Congress cannot unilaterally decide to take their citizenship away, without first amending the Constitution. The amendment does not prevent Congress from enacting laws that confer US citizenship upon other people, also. It's just that those other people would not have constitutional protection of that citizenship.

In order for citizenship to be restricted just to people born or naturalized in the US, the clause in the amendment would have to say "ONLY 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." Then, it would be unconstitutional for Congress to grant citizenship to someone who did not meet those requirements.

Here's an analogy:

Take the statement "All hammers are tools." Nobody would disagree with that statement. But it doesn't mean that screwdrivers or saws aren't also tools. It just means that hammers definitely ARE tools, no ifs, ands, or buts.

Similarly, the statement that "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" does not exclude other people from also being citizens of the United States, it just means that the ones who are born or naturalized in the United States, and subject to the jurisdiction thereof definitely are citizens.

McCain is a citizen through parentage and he has held that citizenship from the moment of his birth.