The antonyms for the phrase "hangs onto hat" could be phrases like "drops the hat," "relinquishes the hat," "discards the hat," or "abandons the hat." These phrases indicate a lack of attachment to the hat, suggesting that the person wearing the hat doesn't care about keeping it safe or holding onto it. Alternatively, phrases like "places the hat carefully," "tucks the hat away," or "stores the hat," imply that the hat is valuable and precious to the wearer, and they take care to ensure it is stored safely. Ultimately, the antonyms for "hangs onto hat" depend on the context and the attitude of the person wearing the hat.