I agree but the other students are just sexist. if they saw that someone else, who is supposed to be inferior than them, is doing much much better than them, then they might start bullying them ( just like Sanghee was pushed by others or attacked by William and his friend for placing first or accused of cheating). the world isn't so fair. she just wanted to avoid others' eyes and stay out of trouble. it is commendable that you would think like that. but others might not.
and freesia is also the daughter of the emperor. there might have been circumstances where the emperor sent freesia as a spy to earn sanghee's trust to like kidnap her or something and freesia would have done that just to get his father's recognition. (which thankfully is not the case).
I just don't really get why she lied about her knowledge and skills. It just seems counterproductive to me. By virtue of existing, she stands out. And on to that her lack of magic and everyone would of course pay attention to a girl who is at the highest level of education in the world they live in but has no apparent special skills. Like, to me, it just would have come across better to outright exceed others so then they would say, "How can a girl be this smart!"
And then, I'm worried that anybody who looks into her actual origins will find out anyway. Then, even if she's found to be smart, she get made into a huge liar. And she hasn't even told Freesia. That's someone who she wants to befriend and she could definitely find out.