The phrase "have a case" implies a certain level of certainty or conviction in one's argument or position. Its antonyms, therefore, might include phrases that suggest a lack of conviction or uncertainty, such as "don't have a leg to stand on," "unclear," or "up in the air." Other antonyms might include phrases that suggest the opposite of having a strong argument or position, such as "unsubstantiated," "unfounded," or "baseless." Overall, the antonyms for "have a case" emphasize a lack of conviction or a weak argument, rather than the strong, persuasive argument implied by the original phrase.