Someone who's insolent is either really doing her own thing, even if it goes against what everyone else is doing, or she’s mildly disrespectful.
That student in your class who is constantly snubbing the teacher, snorting when he gives assignments, and rolling her eyes when he reads passages aloud from your vocabulary textbook? Insolent, definitely insolent. There might be another student who adorns her school uniform with pins and ribbons, cuts her hair shorter than the dress code allows, and rolls her socks down. This student is also insolent, in the sense that she defies the rules.