The phrase "assert its superiority" is correct and usable in written English.
You can use it to refer to a person, organization, or thing emphasizing or declaring their own superiority in relation to something else. For example, "The company asserted its superiority in the industry by introducing several groundbreaking products."
Since the political community is the social unit that can dispose of people's lives, it will be able, where it exists, to assert its superiority over all other social groups within its confines and to rule out violent conflict among its members (CP 37 45).
After all, the average person who thinks about the early 17th century doesn't see a newly emergent merchant class keen to assert its superiority over a landowning elite.
They also likely would feel a strong need to defend the category with which they identify and assert its superiority, a tendency that atheists share.
Why do we need to diminish the greatness of someone who owns up to his society's errors instead of asserting its superiority, and who accomplishes things with patient prodding instead of with bluster and force?
And isn't it really true of all ekphrastic literature, fiction and poetry, that even when it claims to be describing or praising a work of visual art it is in fact asserting its own superiority?
This shame is understandable in the context of the cold war, when the Soviet bloc countries over which the west, with considerable justification, asserted its moral superiority, kept so much secret from their own peoples.
Benedict Cumberbatch is so desperate to assert his superiority over the wonderful horses that he's actually sitting on top of one.
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.
Actually, the concept of the chosen people was never meant to assert Jewish superiority or supremacy, and it certainly doesn't mean that today.
A witty comeback that seeks to assert your superiority or greater status will backfire because it will turn into a matter of the other person insisting that "you think you're too good for me", and so forth, and once you're in this type of argument, things spiral ever out of control.
From this observation, although we could not assert the superiority of undiluted serum over diluted serum eye drops, it implies that 100% serum clinically provides at least as effective as lower concentration drops in enhancing corneal epithelial wound closure and does not seem to have detrimental effects on the healing process.
