No person shall be a Senator or Representative in Congress, or elector of President and Vice President, or hold any office, civil or military, under the United States, or under any State, who, having previously taken an oath, as a member of Congress, or as an officer of the United States, or as a member of any State legislature, or as an executive or judicial officer of any State, to support the Constitution of the United States, shall have engaged in insurrection or rebellion against the same, or given aid or comfort to the enemies thereof. But Congress may, by a vote of two-thirds of each House, remove such disability.

That is the 14th amendment, it clearly states that if any officer of the United States [which can be civil or military] engages in insurrection, they cannot be elected for President.

So exactly how in the actual fuck is the "Chief Executive Officer of the Executive Branch of the United States" not an officer of the United States??

https://papers.ssrn.com/sol3/papers.cfm?abstract_id=4591133

Page 17:

V. The persons who framed Section Three of the Fourteenth Amendment regarded the President of the United States as an officer of the United States

The President of the United States was among the officials who took the oath to the Constitution that under Section Three triggered disqualification for participating in an insurrection. As noted in the previous section, the persons responsible for the Fourteenth Amendment sought to bar from present and future office all persons who betrayed their constitutional oath. “All of us understanding the meaning of the third section,” Senator John Sherman of Ohio stated, “those men who have once taken an oath of office to support the Constitution of the United States and have Fourteenth Amendment distinguished between the presidential oath mandated by Article II and violated that oath in spirit by taking up arms against the Government of the United States are to be deprived for a time at least of holding office.” No member of the Congress that drafted the the oath of office for other federal and state officers mandated by Article VI. Both were oaths to support the Constitution. Senator Garrett Davis of Kentucky saw no legal difference between the constitutional requirement that “all officers, both Federal and State, should take an oath to support” the Constitution and the constitutional requirement that the president “take an oath, to the best of his ability to preserve, protect, and defend the Constitution.” Senator James Doolittle of Wisconsin declared that Congress need not pass laws requiring presidents to swear to support the Constitution because that “oath is specified in the constitution.”

In fact, the exact question of whether the disqualification from public office covered the Presidency came up at the time the Fourteenth Amendment was being drafted: https://crsreports.congress.gov/product/pdf/lsb/lsb10569

Specifically:

One scholar notes that the drafting history of Section 3 of the Fourteenth Amendment suggests that the office of the President is covered:

During the debate on Section Three, one Senator asked why ex-Confederates “may be elected President or Vice President of the United States, and why did you all omit to exclude them? I do not understand them to be excluded from the privilege of holding the two highest offices in the gift of the nation.” Another Senator replied that the lack of specific language on the Presidency and Vice- Presidency was irrelevant: “Let me call the Senator’s attention to the words ‘or hold any office, civil or military, under the United States.’”

I’ll highlight that last bit again:

Another Senator replied that the lack of specific language on the Presidency and Vice- Presidency was irrelevant: “Let me call the Senator’s attention to the words ‘or hold any office, civil or military, under the United States.’”

That is from this paper: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3748639

Some people seem to have a lot of trouble with figuring out what "or" means, in a list of things.

My understanding is that he isn't running for office yet. He's running for a party's nomination for president.

If he wins that, then he's running for president and states will have to decide whether he can be on the ballot.

I know it's a fine distinction, but if they ruled otherwise, it would get overturned.

Jokes aside, the fact that the President as commander-in-chief is a civilian and not an officer of the military is actually quite fundamental to civilian control of the military in the USA.