56 Moby Thesaurus words for "cross purposes": agreement to disagree, antagonism, antipathy, antithesis, bad blood, clashing, collision, competition, conflict, confrontation, contradiction, contradistinction, contraindication, contraposition, contrariety, contrariness, contrast, counterposition, difference, difference of opinion, difficulty, disaccord, disagreement, discrepancy, disparity, dissension, dividedness, division, enmity, fractiousness, friction, hostility, inconsistency, inimicalness, misunderstanding, negativeness, noncooperation, obstinacy, odds, oppositeness, opposition, opposure, oppugnance, oppugnancy, perverseness, perversity, polarity, polarization, recalcitrance, refractoriness, repugnance, rivalry, showdown, uncooperativeness, variance, vying

Source: Moby Thesaurus II by Grady Ward, 1.0