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Definition of disagreement : 1. A falling out, or controversy; difference.
2. Difference of opinion or sentiment.
3. The state of disagreeing; a being at variance; dissimilitude; diversity.
4. Unsuitableness; unadaptedness.

Synonyms:

deviation, contestation, variability, incongruity, dissimilarity, firestorm, nonconcurrence, agree, a war of words, divergency, difficulty, spat, polemic, cross fire, battle royal, contrast, otherness, variant, dissimilitude, distinction, discrepancy, disputation, distinctness, distinctiveness, rhubarb, racket, inconsistency, scrap, kickup, a world of difference, inequality, contrariety, tiff, variety, discrepance, set-to, distance, unlikeness, disparateness, bicker, disparity, variance, division, departure, falling-out, noise, argle-bargle, variableness, dissensus, run-in, diversity, tangle, diverseness, contretemps, variation, word, donnybrook, debate, discrimination, gap, argy-bargy, divergence

disaccord, divisiveness, complaint, argument, nonagreement, repudiation, rejection

contest, break, misunderstanding, jarring, clashing, breach, quarreling, ill will, rupture, split, vendetta, wrangle, competition, disunion, controversy, battle, quarrel

brawl, contention, commotion, enmity, cacophony, animosity, disharmony, warfare, feud, dissidence, hassle, strife, collision, dissension, clamor, difference, riot, dissonance, raucousness, clash, hubbub, altercation, harshness, imbroglio, squabble, tension, squall, antipathy, hostility, row, discord, discordancy

dissent, discordance, incompatibility, disunity

disdain, disinclination, denial, declination, dismissal, renouncement, refusal

contradiction, suppression, adversary, conflict, repression, friction, inhibition, counterattack, opposition, dispute, protest, confrontation, hindrance, counteraction, antagonism, interference, impediment, obstinacy, obstruction, rebuff, objection, defiance, repulsion, challenge, fight, resistance

Usage examples:

• It is almost the only point of disagreement I have with that admirable woman. - "Pebbles on the Shore", Alpha of the Plough (Alfred George Gardiner).
• There was fatal disagreement between the general and Saltonstall. - "Nooks and Corners of the New England Coast", Samuel Adams Drake.
• Reflecting upon their disagreement I recall that about an hour ago Jake, with an apologetic " Excuse me!" - "The Discovery of Yellowstone Park", Nathaniel Pitt Langford.