The phrase "were best behavior" typically refers to a state of good behavior, politeness, and appropriate conduct. Antonyms for this phrase would include words and phrases like "misbehaving," "improper conduct," "rudeness," "being disrespectful," "acting out," "impoliteness," "discourteous behavior," and "being ill-mannered." Essentially, any behavior that is contrary to being on one's best behavior would qualify as an antonym. The opposite of being on one's best behavior would imply that an individual is acting in a way that is not socially acceptable, and is failing to adhere to basic standards of civility and decorum.