Being consonant with is a phrase that implies agreement or harmony between two or more things. Therefore, its antonyms would be contradictory or incompatible. If two things are contradictory, they are opposite in nature and cannot coexist harmoniously. Incompatible, on the other hand, refers to things that cannot be combined or used together without conflict. Other antonyms for being consonant with include opposing, disagreeing, contradicting, clashing or negating. In certain situations, it may be important to identify antonyms for being consonant with to avoid confusion or misunderstandings between parties.