So if you get arrested in Mexico, does that mean you are a Mexican?
Only if you were born there.
Again, my argument is not that illegal immigrants are citizens, but that persons born on US soil are citizens.
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.
Just because someone is subject to US jurisdiction does not mean that he is a citizen.
But if he is either born or naturalized in the US and is subject to US jurisdiction, then he is.
It is clear that illegal aliens are subject to US jurisdiction - otherwise, the US would not be able to enforce its own laws within its own borders.
Their children in the US are also subject to US jurisdiction and if they born here they are citizens, meeting both of the core requirements for citizenship established in the 14A.