That would be a big fat NOPE.

I would be okay paying for the cancellation if there was a pre-existing policy, but there's absolutely no reason a therapist should be asking for a doctor's note. I mean, there are plenty of times when I'm too ill to get to an appointment but not ill enough to bother going to see my doctor. Even if I go see a doctor, that's really not something my therapist should need proof of. I mean, trust is such a basic component of the therapeutic relationship, and that demand would indicate to me that the therapist didn't believe me. Plus, as others have pointed out, you employ the therapist, not the other way around. It's your right to cancel for whatever reason you want. You shouldn't be asked to justify that.