Alice,
There are no set rules for driving instructor/learner confidentiality as such (compared to patient/doctor relationship) but a good driving instructor should keep each learner's weaknesses and strengths to himself really. An instructor can use examples where mistakes have been committed by learner drivers he's teaching (or has taught in the past) to illustrate a point but without naming the student in question.
As I always say, if you have
doubts about your instructor's ability to teach (whether it's professional or just social), it is best to change to another one who has been recommended by somebody reliable.