Taking out after refers to pursuing and attacking someone or something. The antonyms for taking out after would be terms like retreat, surrender, and avoidance as they all describe removing oneself from a dangerous or unpleasant situation. Similarly, alternative antonyms could include ignoring, neglecting, or dismissing someone or something. These words all indicate a lack of action or interest, which stands in contrast to taking out after. Overall, the opposite of taking out after entails choosing to disengage or step back, rather than pursuing or attacking something or someone.