The phrase "are the case" typically implies that something is true or accurate. Therefore, antonyms for this phrase could include "aren't the case," "are false," "are incorrect," "are invalid," or "are inaccurate." Essentially, any word or phrase that conveys the opposite meaning of truth or accuracy could be considered an antonym for "are the case." It's important to use antonyms carefully and thoughtfully, as the wrong word or phrase could actually imply the opposite meaning of what is intended. In any case, understanding antonyms and how they can be used effectively is an important skill for any writer or communicator.