Earlier quoted context omitted.
In this case, the president does not have the authority under the constitution to purport to invalidate the citizenship of natural-born citizens. It is the executive that broke the proper functioning of the government.
Your news sources have woefully misinformed you. Trump's argument is that it's not enough to be born here, you have to also be a charge of the country: "Section 1. 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." Note the "and subject to the jurisdiction thereof". Trump's argument is that people born…
Sen. Edgar Cowan of Pennsylvania said "I am really desirous to have a legal definition of ‘citizenship of the United States. Is the child of the Chinese immigrant in California a citizen?" He didn't think that child should be.
Sen. Conness of California said he thought it should cover "the children begotten of Chinese parents in California, and it is proposed to declare that they shall be citizens. I voted for the proposition to declare that the children of all parentage whatever, born in California, should be regarded and treated as citizens of the United States, entitled to equal civil rights with other citizens of the United States." And let's remember, as Conness was certainly aware, that many of those Chinese laborers had been imported illegally.
They knew what they were passing, and they knew it included birthright citizenship. Senators who wanted to alter the Amendment to exclude some people failed.