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.
late 14c., "interchangeable," from Old French convertible "interchangeable" (13c.) and directly from Late Latin convertibilis "changeable," from Latin convertere "to turn around; transform," from assimilated form of com "with, together" (see con-) + vertere "to turn" (from PIE root *wer- (2) "to turn, bend").
Meaning "capable of being changed in form, substance, or condition" is from 1530s. Of paper money, etc., "capable of being converted into gold of a similar amount," from 1834. The noun is recorded from 1610s; meaning "automobile with a fold-down top" is from 1916. Related: Convertibility.
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Harper, D. (n.d.). Etymology of inconvertible. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/inconvertible