[Non-Sequitur]

The children of illegal aliens are most certainly NOT "subject to the jurisdiction thereof", and are NOT US citizens by circumstance of birth on American soil.

Yes they are. Subject to the jurisdiction means subject to our laws. Regardless of whether they are here legally or illegally, the immigrant can be arrested if they violate the law. Contrast that with a foreign representative protected by diplomatic immunity and not subject to the laws.

[Windflier]

Subject to the jurisdiction means subject to our laws. Regardless of whether they are here legally or illegally, the immigrant can be arrested if they violate the law.

We disagree.

I interpret the meaning of the phrase "and subject to the jurisdiction thereof" to indicate that a person is bound to a nation by birth, or naturalization of their citizenship.

That does not mean that such a person cannot be arrested for breaking our laws while in our country. Any recognized foreigner can be, and would be, in any foreign country, including America.