'Promote' is Latin for 'move forward' — and 'demote' wasn't coined until 1881. A remarkably late back-formation.
To advance someone to a higher position or rank; to support or actively encourage a cause, process, or venture; to publicize a product or event.
From Latin 'prōmōtus,' past participle of 'prōmovēre' (to move forward, to push onward, to advance in rank or position), composed of 'prō-' (forward, on behalf of, in favour of) + 'movēre' (to move, to set in motion, to stir). The PIE root behind 'movēre' is *mew- (to push, to push away, to set in motion), which generated Latin 'movēre' and its entire family: 'mōtus' (motion, movement — 'motor,' 'motion'), 'mōtīvus' (causing motion — 'motive'), 'mōmentum' (the force that moves, a brief interval — 'momentum,' 'moment'), 'commovēre' (to move together, to stir up — 'commotion'), 'removēre' (to move back — 'remove'), and 'ēmovēre' (to move out or away — 'emotion' — to be 'moved out' of one's usual state). The English