The act of curling one's lip is often associated with disgust, contempt or disdain. Antonyms for this expression could, therefore, include curling one's lip in pleasure or admiration, or simply smiling or grinning instead. Other possible opposites might include remaining neutral, showing empathy, or expressing interest or curiosity. Depending on the context, different phrases or words might be appropriate, such as praising, complimenting, or nodding in agreement. Ultimately, the opposite of curling one's lip will depend on the specific situation and the speaker's intended message or emotion.