Section 3 of the 14th Amendment does not cover the President. The position is purposefully omitted from that section which mentions only “ELECTORS OF THE PRESIDENT”. Furthermore the President has never been considered “AN OFFICE UNDER THE UNITED STATES” (see David McKnight, The Electoral System of the United States, 1878).
Federal elected officials in the Executive and Legislative branches are not offices under the United States and that is why Senators and Representatives are distinctly and separately mentioned in Section 3, Article 14.
Unfortunately Sec. 3 when it speaks of individuals who may have "engaged in insurrection or rebellion" doesn't say how that is determined--does the person have to be found guilty in a court of law or is it enough for a Congressional committee (consisting entirely of that person's political enemies) to assert the person's guilt? Of course in the Reconstruction era it was obvious who was meant.