natural born citizen is a subset of US citizen
No, there is no such distinction. It doesn't exist. Again, let me allow you to read the pertinent portion of the sentence that devastates your attempt to twist this idea to your liking:
contemplates two sources of citizenship, and two only,-birth and naturalization.
That line states crystal clear that the Constitution recognizes only if a person is born with citizenship or is naturalized as a citizen after birth.
There is no 'subset' to discuss. There is no 'subset' that exists. If you are a citizen at birth you are a citizen at birth. And if you are a citizen at birth, you are a 'natural born citizen'.
Period. End of story. Don't like it? Take it up with the Supreme Court. They are the ones who wrote it.
This was a ridiculous argument when people tried it against Obama and it was a ridiculous argument when people tried it against Chester Arthur and it was a ridiculous argument when people tried it against Charles Curtis and it remains a ridiculous argument against Ted Cruz. The reason why it is ridiculous is that being born a citizen makes you a natural born citizen. The idea that there is a magic third form of citizenship (or the idea that it is a specific 'subset' of someone born a citizen) is not based on anything found in the laws or jurisprudence of the United States.
No, there is no such distinction. It doesn't exist.
if there is no distinction... then why did the founders bother to make the requirement in A2S1?
their point was to insure a foreign king could not assume the office. this is why the person had to be natural born so that there was no foreign allegiance, at least by birth.
using your 'logic', any anchor baby could be POTUS. william and kate could fly to NYC, have a kid, fly back and that kid would be a natural born US citizen as well as the next king of england. the EXACT situation the founders were looking to avoid.
as for the supreme court, they've discussed it four times. each time recognizing both parents and on the soil as the requirement.
http://www.fourwinds10.net/siterun_data/government/us_constitution/news.php?q=1308252582
but hey, you keep ignoring the obvious and keep going on about how 'your guy' is special and is eligible, completely ignoring the Constitution