Do therapists argue about their fee during sessions?

If things actually went down as you say they did, your therpist was very unprofessional. I would think she should have sent out a very formal letter stating that as of such and such a date, she would be raising her fee to $100.00. Hopefully, you would be able to continue as a patient, but if you couldn't, she would understand. She should never have brought it up during your session. And yes, doctors charge for missed visits. Get a new therapist and move on.