"Have swing at" means to attempt or try something, typically in a forceful or aggressive manner. Antonyms for this phrase could include "abstain," "forgo," or "refrain," which all suggest a deliberate decision to not engage in an action. Other antonyms might include "hesitate," "dither," or "procrastinate," which suggest a lack of confidence or readiness to act. Alternatively, one could use opposites such as "embrace," "emphasize," or "applaud," which suggest a positive and enthusiastic approach to an action, rather than a defensive or combative one. Overall, the antonyms for "have swing at" suggest a range of attitudes and behaviors, from deliberate restraint to active enthusiasm.