Her whole family is bad, but so is the sensei in a sense.. She literally created a fake identity Kohaku is getting dependent on, even if she were to suspect something that's not changing the fact 😐..
All that just because she's embarrassed about what she likes, which isn't excusing toxic behaviour 😶..
To be fair, she isnt quite doing anything wrong/sus... at least by now.
I mean, she has been a good role model for this girl and helping her to be truthful and work on the stuff she likes instead of the things her parents want for her.
Really the bad part is that sensei is lying... Though that was probably worsened by that scene where sensei heard a teacher getting in problems for meeting with a student outside classes. After that there were probably few options in her mind, either
1) stops any contact with the girl all together, knowing that will impact negatively this girl's life, or
2) she keeps with the lie to keep herself protected so she cant get in problems for tutoring/hanging out with the girl outside class.