Curl (one's) lip phrase
To move the corner of one's lip upwards to show you think that someone is contemptible.
She'll probably curl her lips at my new jeans because they're cheap
When I walked in, she looked at me from head to toe and curled her lip.
That kid is curling his lip at your magic trick!
To reject someone or something because you think they do not deserve your interest or respect
The verb "curl" must be conjugated according to its tense.
The origin of this phrase is not clear.
To quit; to give up, stop doing something because you know that you cannot succeed; admit defeat
The team is not going to throw in the towel just because they lost one game.