The phrase "giving a whirl" typically means to try something out or attempt to do something. The antonyms for this phrase may include words like avoid, neglect, or abstain. These words imply a lack of effort or interest in trying something new. For example, if someone says, "I'm going to avoid giving skiing a whirl this winter," it means they have no intention of trying skiing. Another antonym could be giving up, which means to quit or abandon something before giving it a chance. When faced with a new opportunity, it's important to keep an open mind and avoid these negative antonyms.