The phrase reads, "All persons born or naturalized in the United States, and subject to the jurisdiction thereof...

The "and" is there for a reason. It implies that it's possible for only one of those things to be true.

It also implies that both cases must be true before one is considered a U.S. citizen.

So: You could be born in the U.S. but not subject to its jurisdiction.

As in: Your parents are citizens of one or more other nations and therefore subject to that jurisdiction. That makes you, as their child, also subject to that same jurisdiction. Which is not the United States.

That's why just being born on U.S. soil is not enough to make you a citizen.