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.
early 15c., sincerite, "honesty, genuineness," from Old French sinceritie (early 16c., Modern French sincérité) and directly from Latin sinceritatem (nominative sinceritas) "purity, soundness, wholeness," from sincerus "whole, clean, uninjured," figuratively "sound, genuine, pure, true, candid, truthful" (see sincere).
1620s (implied in insincerely), from Latin insincerus "spoiled, corrupted; not genuine, not pure, adulterated," from in- "not" (see in- (1)) + sincerus "genuine, candid" (see sincere). Related: Insincerely.
<a href="https://www.etymonline.com/word/insincerity">Etymology of insincerity by etymonline</a>
Harper, D. (n.d.). Etymology of insincerity. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/insincerity