The phrase "makes a big thing about" denotes an excessive, exaggerated, or unnecessary attention to something that could be trivialized, minimized, or ignored. Antonyms for this phrase would be "downplay," "underplay," "minimize," "deemphasize," "trivialize," "overlook," "neglect," or "ignore." These antonyms suggest that the subject of the attention is not worth the energy or attention that is being given to it. Instead, these antonyms suggest a more balanced, objective, or realistic approach to the situation at hand. By using these antonyms, we can avoid creating unnecessary drama, tension or anxiety and focus on what really matters in a given situation.