The term "has a swing at" typically means to take a crack at something, whether it be a task, job, or even an opponent in combat. Antonyms for this phrase could include avoiding, shying away from, or even refraining from participating altogether. Sometimes, it may be better to exercise caution and restraint, especially if the task at hand is risky or outside of one's expertise. Additionally, showing humility and accepting help from others could be considered an antonym for "having a swing at," as opposed to stubbornly trying to do everything oneself. In short, antonyms for this phrase revolve around avoiding or accepting limitations and seeking help when necessary.