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. No State shall make or enforce any law which shall abridge the privileges or immunities of citizens of the United States; nor shall any State deprive any person of life, liberty, or property, without due process of law; nor deny to any person within its jurisdiction the equal protection of the laws.
The contention is around and subject to the jurisdiction. It can mean that all people born in the US or to US citizens are default subject to US jurisdiction. You likely want to argue that people are only citizens if they are subject to the jurisdiction.
But for the 2nd interpretation, you also need to define what being "subject to the jurisdiction thereof" means somewhere else, which the constitution does not. As it stands, it's always been interpreted as an addendum: you are born in the US or to citizens, therefore you are subject to its laws.
This is clear in not other place than Taxes: the United States is only one of two nations in the world with a citizenship income tax. When I lived over seas I had to file every year. It'd often amount to $0 (the US grants an exception up to like $90k or something if you don't live in the US), but if you make too much, you get taxed twice. Not paying double tax is the number one reason people renounce their US citizenship if they have two.
Finally, even if the amendment is not clear, the executive does not have the power to change naturalization processes. As I said, ArtI.S8.C4.1 clearly defines congress has that power. So no Trump does not have the power to do this via EO. It will get struct down on the basis of ArtI.S8.C4.1 alone. If the people want it without an amendment, they need to get their corrupt, shitty senators and congressmen to attempt it. Only then would the courts even bother to deal with the 14th amendment issue.