To be literal, high is an adjective used of people, institutions and qualities that are worthy of respect, honour and admiration.
Conversely, we use “low” when the opposite of these things are merited: contempt, shame and disgust (or something like these).
The presidency is among the highest offices in the USA - arguably the highest,
Accordingly, the conduct of the holder of that office is expected to show the qualities that match that office (I decline to specify what they are, to keep out of politics.
If, Instead, a president should conduct him or herself in a manner that was (say) dishonourable or dishonest, his or her conduct could be said to fall below the high standard expected of a person holding high office.
The preposition merely continues the metaphor. As to the office holder named in the question, I could not possibly comment,