The phrase "give a whirl" means to try or attempt something. The antonym for this phrase would be to refrain from trying or to simply not attempt something. Other antonyms could include avoiding, rejecting, or disregarding an opportunity to try something new. Additionally, giving up or quitting would also be opposites of "giving a whirl." Sometimes it's important to know when not to give something a whirl, whether it's due to lack of interest, fear of failure, or prioritizing other responsibilities. Ultimately, it's up to the individual to decide when to give something a try and when to hold back.