No one is suggesting that there is a third "type" of citizenship. Take that one off of your argument list.
Birthright citizenship is NBC.
That is a non sequitur. Your conclusion does not follow from your previous assertion. Birthright citizenship flowing from nature makes a "natural" citizen, but birthright citizenship flowing from a man made statute does not. The statutory form of citizenship is imminently malleable by the whim of congress, and there is nothing "natural" about it.
There is no argument because there is no legal authority that agrees with you
Which has nothing to do with anything. "Authorities" have been wrong so many times, the wonder is that they ever get anything right. Again, I point to Abortion and "gay" Marriage as examples of "Authorities" being wrong.
and you can quote Vattel until you turn purple but you will continue to be ridiculed mercilessly.
What does being correct have to do with people agreeing with me or not? "People" thought Obama was a good idea.
"People" are often stupid and often wrong, so I don't really pay a lot of attention to what ignorant "people" think about anything.
Is this the best you can do for an argument? You haven't advanced anything intellectually relevant, and i'm beginning to think you can't.
That is a non sequitur.
It most certainly is not. You can't just wish away reason. There are 2 types of citizenship: naturalized and natural born. Anyone with birthright citizenship does not require naturalization and is therefore by definition a natural born citizen.
Obviously there is no point in arguing with someone who thinks everyone else on the planet is wrong. The best way for you to win the argument is in a court of law. I beseech the birther community to either win in court or let it rest. Sadly, neither of those things will happen.