The phrase "assert his superiority" is a correct and usable part of a sentence in written English.
It means to confidently and forcefully demonstrate one's higher status or authority over others. Example: The CEO constantly tries to assert his superiority over his employees by delegating menial tasks and taking credit for their work.
As the standoff unfolds, Fugard shows us how Hal, by asserting his superiority, forces that shame out of himself and into Sam.
A passage in the later Book of the Dead (1200 bce) represents the deceased, who has been ritually identified with Osiris, declaring that he comprehends the whole range of time in himself, thus asserting his superiority to it.
But in truth the two-horse race looked more like a one-man show last night as the world No1 asserted his superiority over his challengers, Harrington included, at 2009 US PGA Championship at Hazeltine and challenged history to prove him wrong.
Moreover, his muscles and balance convey an upward movement, as if he is growing out of her, although he is above Mary, asserting his superiority to her.
When confidence and adrenaline are on the charge, the striker's instinct is to trust in power and assert his physical superiority by ramming the ball past the keeper.
At different moments he understands his compulsion in different ways: a pre-emptive defence against rejection, a means of asserting his moral superiority over others, even a form of self-anesthetisation: He was, he thought, very close to the ideal state he dreamed of in his reading, the state of renunciation and quiet.
To assert his status, the tribe's chief picks up one of the celebrated anthropologist's pads and starts scribbling on it, to impress his subjects with his superiority.
But Schmidt has done little to assert his authority.
But Prince Ahmed might still assert his seniority by age.
The basic plot of Robert Bresson's "Pickpocket," from 1959 (playing at Film Forum on Aug. 20), is derived from that of "Crime and Punishment": an isolated and severe young man (Martin LaSalle) becomes a philosophical criminal who asserts his sense of superiority in larcenous acts while also longing to be caught.
