I would be curious about your life (because i'm a nosy cow), but it wouldn't put me off and I wouldn't stop having lessons with you. I would have felt the same 10 years ago when I was 17 too. But then I am very liberal. One of my driving instructors is also thinking of quitting due to a lack of pupils, maybe it isn't as personal as you think?
Good luck anyway, its horrible to feel that something so personal is holding your career back.