late 14c., "incapable of being bent, physically rigid," also figuratively, "unyielding in temper or purpose," from Old French inflexible and directly from Latin inflexibilis "that cannot be bent," from in- "not, opposite of" (see in- (1)) + flexibilis "pliant, yielding" (see flexible). In early 15c. an identical word had an opposite sense, "capable of being swayed or moved," from the other in- "in, on" (see in- (2)). Related: Inflexibly.
-ity
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]