The phrase "be on one case" implies that someone is being persistent and determined in pursuing a particular issue or individual. Some antonyms for this phrase might include "back down," "give up," or "let go." These terms suggest a sense of surrender or resignation rather than active engagement. Other antonyms might include "ignore," "disregard," or "abandon," which suggest a lack of interest or concern. Whatever the context, understanding antonyms can be helpful in developing a richer vocabulary and a more nuanced understanding of language. By exploring different shades of meaning, we can communicate more effectively and connect more deeply with those around us.