inflexibility (n.)

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.

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]