The phrase "are one's case" refers to being convinced or having a strong argument in support of something. Antonyms for this phrase could include words or phrases such as "disproved," "refuted," "invalidated," "discredited," "unconvincing," "unpersuasive," "weak," or "inadequate." These antonyms can be used to express the opposite of being convinced or having a strong argument in support of something. For example, one might say "The evidence presented has disproved your case" or "Your argument was weak and unpersuasive." Understanding antonyms can help to better communicate and express opposing viewpoints in debates or discussions.