The phrase "waves around" generally means to brandish or display something flamboyantly. Antonyms for this phrase include hiding, concealing, covering, and keeping to oneself. These words suggest a sense of privacy, modesty, or discretion. Instead of waving something around for everyone to see, antonyms for this phrase suggest a desire to keep things private or reserved. For instance, instead of waving around one's wealth, one might choose to conceal it for fear of attracting unwanted attention. Similarly, instead of waving around one's emotions, one might choose to keep them in check and maintain a level of professionalism or stoicism.