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 meaning "not, opposite of, without" (also im-, il-, ir- by assimilation of -n- with following consonant, a tendency which began in later Latin), from Latin in- "not," cognate with Greek an-, Old English un-, all from PIE root *ne- "not."
In Old French and Middle English often en-, but most of these forms have not survived in Modern English, and the few that do (enemy, for instance) no longer are felt as negative. The rule of thumb in English has been to use in- with obviously Latin elements, un- with native or nativized ones.
"accountable for one's actions, answerable" to another, for an act performed or its consequences, 1640s, from obsolete French responsible (13c., Modern French responsable, as if from Latin *responsabilis), from Latin respons-, past-participle stem of respondere "respond, answer to, promise in return," from re- "back" (see re-) + spondere "to pledge" (see sponsor (n.)).
The meaning "reliable, trustworthy" is from 1690s. It retains the sense of "obligation" in the Latin verb. Related: Responsibly.
With regard to the legal use of the word, two conceptions are often confused — namely, that of the potential condition of being bound to answer or respond in case a wrong should occur, and that of the actual condition of being bound to respond because a wrong has occurred. For the first of these responsible is properly used, and for the second liable. [Century Dictionary]