The phrase "make a big thing about" often implies an overreaction or excessive focus on something. Antonyms for this expression might include "downplay," "minimize," or "understate." These words suggest a more reserved or measured approach to a situation, perhaps not drawing too much attention or causing unnecessary drama. Other antonyms could include "ignore," "dismiss," or "disregard," which imply a lack of concern or emphasis altogether. Alternatively, one could use more positive antonyms, such as "celebrate," "highlight," or "emphasize," to suggest a more celebratory or meaningful approach to an event or situation.