disagree v.

word-forming element of Latin origin meaning 1. "lack of, not" (as in dishonest); 2. "opposite of, do the opposite of" (as in disallow); 3. "apart, away" (as in discard), from Old French des- or directly from Latin dis- "apart, asunder, in a different direction, between," figuratively "not, un-," also "exceedingly, utterly." Assimilated as dif- before -f- and to di- before most voiced consonants.

The Latin prefix is from PIE *dis- "apart, asunder" (source also of Old English te-, Old Saxon ti-, Old High German ze-, German zer-). The PIE root is a secondary form of *dwis- and thus is related to Latin bis "twice" (originally *dvis) and to duo, on notion of "two ways, in twain" (hence "apart, asunder").

In classical Latin, dis- paralleled de- and had much the same meaning, but in Late Latin dis- came to be the favored form and this passed into Old French as des-, the form used for compound words formed in Old French, where it increasingly had a privative sense ("not"). In English, many of these words eventually were altered back to dis-, while in French many have been altered back to de-. The usual confusion prevails.

As a living prefix in English, it reverses or negatives what it is affixed to. Sometimes, as in Italian, it is reduced to s- (as in spend, splay, sport, sdain for disdain, and the surnames Spencer and Spence).

late 14c., "to give consent, assent," from Old French agreer "to please, satisfy; to receive with favor, take pleasure in" (12c.), a contraction of the phrase a gré "favorably, of good will," literally "to (one's) liking," or a like contraction in Medieval Latin. The French phrase is from a "to," from Latin ad (see ad-) + Old French gre, gret "that which pleases," from Latin gratum, neuter of gratus "pleasing, welcome, agreeable" (from suffixed form of PIE root *gwere- (2) "to favor").

In Middle English it also meant "to please, gratify, satisfy," a sense preserved in agreeable. Of parties, "come to agreement; make a settlement," mid-15c.; the meaning "to be in harmony in opinions" is from late 15c. Of things, "to coincide," from 1520s. To agree to differ is from 1785 (also agree to disagree, 1792). Related: Agreed; agreeing.

late 15c., "refusal to agree or assent," from disagree + -ment. From 1570s as "difference in form or essence," also "difference of opinion or sentiments," perhaps a separate formation from dis- + agreement. From 1580s as "a falling out, contention." As "unsuitableness, unfitness," by 1702.