1640s, "not legally answerable for conduct or actions," from assimilated form of in- (1) "not, opposite of" + responsible. Meaning "not acting with a sense of responsibility" is from 1680s. Related: Irresponsibly.
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]
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Definitions of irresponsibility
a form of untrustworthiness; the trait of lacking a sense of responsibility and not feeling accountable for your actions;