The phrase "to art one's case" refers to presenting and arguing one's point of view or side of an argument in a clear and convincing manner. Antonyms for this phrase would include being vague or unclear about one's position, failing to make a strong argument, or avoiding the topic altogether. Other antonyms could include conceding or giving up on one's position without a fight, accepting defeat without presenting any counterarguments, or simply remaining passive in the face of opposition. Ultimately, the opposite of "to art one's case" would be to fail to effectively communicate one's perspective and to give in to opposition without putting up a fight.