incompatibility (n.)

"that cannot coexist or be conjoined," mid-15c., from Medieval Latin incompatibilis, from in- "not, opposite of" (see in- (1)) + compatibilis (see compatible). Originally of benefices, "incapable of being held together;" sense of "mutually intolerant" is from 1590s. Related: Incompatibly.

word-forming element making abstract nouns from adjectives and meaning "condition or quality of being ______," from Middle English -ite, from Old French -ete (Modern French -ité) and directly from Latin -itatem (nominative -itas), suffix denoting state or condition, composed of -i- (from the stem or else a connective) + the common abstract suffix -tas (see -ty (2)).

Roughly, the word in -ity usually means the quality of being what the adjective describes, or concretely an instance of the quality, or collectively all the instances; & the word in -ism means the disposition, or collectively all those who feel it. [Fowler]