despite presenting herself as this amazing, strong, confident girl who can handle anything, she does suffer what most people suffer from and that's self-confidence. again, she may appear confident but that's just an image she projects for others to see. she admits that she never went all the way from Scotty boy but she feels like she can be open about herself with Null who chooses to help her overcome her problems
At the start Jean is pretty much a classic insecure arrogant archetype (my designation). She acts pretty full of herself (but not overwhelmingly so, unlike most people in this kind of archetype), but is actually insecure. In her case she has some good reasons for it, and actually starts to get better about it, which is again better than most people of this archetype.
Jean has - from somewhere - had a lot of pressure placed on her, an expectation to be perfect. I would guess the thinking was a combination of her beauty, brains, and incredible power has caused those around her to have unrealistic expectations of her. Or that is how she sees it at least, that everyone has these high expectations of her.
She even says once "I'm supposed to be perfect". This is a lot to put on anyone, coupled with her powers that she starts to lose control of, and having some of her powers locked away - which makes her feel like she isn't good enough - and... well, a bunch of other stuff, it's no surprise that inside she is actually insecure, maybe even developing imposter syndrome (ironically common among people who actually are capable, while people who aren't have a tendency to Dunning-Kruger). By Summer (almost a year in which we've only seen almost montage level compression of events) she starts to realize this is all bullshit. Null helps her become truly confident in herself, without having to be perfect.
I kinda know what this is like. Aeons ago, when the dinosaurs still roamed the Earth, when I was in high school I somehow got this reputation as being really smart. I never really felt it, I never thought I was stupid, and I certainly knew people I did think were stupid, but I also knew several people I thought were WAY smarter than me. For a time I sort of did have this conflict between what I was doing and what people said I should be capable of, and it was annoying. But the difference here is that I am fundamentally lazy and unwilling to put in a lot of work for something I didn't feel - and come on, how many kids really believe school is that important? Some sure, but not most. So it didn't take long for me to go, 'whatever' and just do my own thing and pretty much ignore what others expected of me. But if I had been someone willing to put in the work, or thought that school was super important, I could easily have fallen into the same trap as Jean - except I don't think I had her brains to back it up.