After the Civil War some people argued that freed slaves were not citizens, because they didn’t enjoy citizenship as slaves. The first part of the 14th was written to grant citizenship to slaves. Unlike illegal aliens slaves were “subject to the jurisdiction” of the United States government.
The people who argue that illegal aliens are “subject to the jurisdiction” of the United States government are trying to bypass the fact that aliens are subject to a different set of rights under our legal system than citizens. For instance, the government can’t deport me. I’m a citizen.
This defeats the jurisdiction excuse.