The opposite meaning of "be consonant with" can be described as "inconsistent" or "discrepant". When something is inconsistent, it does not match or comply with a set of expectations or standards. It indicates a lack of harmony or agreement between two things. Discrepant, on the other hand, means having a significant difference or disagreement in some critical aspects, such as ideas, opinions, or positions. These antonyms can be useful in describing situations where there is a disconnect between two parties, ideas or actions that are not aligned, as well as things that do not conform to a certain standard or expectation.