The antonyms for the phrase "take out after" would be terms that suggest a lack of pursuit or effort to capture someone or something. Words such as ignore, neglect, abandon, or disregard may be used to express the opposite of aggressively chasing after a person or object. Other antonyms could be to let go, release, or surrender. These words illustrate a lack of interest in attaining or following something, instead promoting a more passive approach. In contrast, take out after suggests a proactive attitude that is determined to catch or achieve a goal. Understanding antonyms is just as important as understanding synonyms, as they offer a more complete picture of language comprehension.