Please review section 1 of the 14th amendment, then get back to us with your interpretation of what it means.
America is one of those weird places, were you can break the law by being here illegally, and give birth and gain benefits. That's nuts.
citizenship clause of the 14th amendment:
“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.”
children of citizens and legal immigrants are subject to the jurisdiction of the US. these are people who can be called for the draft, jury selection, etc. this does not include tourists or anyone in the US temporarily as they are the jurisdiction of their home country.
in this regards, illegals would be considered tourists and their children not eligible for citizenship. if they were then it’d be possible for the king and queen of England to be in the US when the queen gives birth... at which point their child could have US citizenship and potentially become POTUS and king at the same time. this is the situation the Founders wanted to specifically guard against hence the natural born citizenship clause.