I don't know all the details in your story. It kind of sounds like there were two different issues going on in your situation at the same time.

First, the therapist's missing of your appointment which was inconvenient for you. Sounds like she took responsibility by admitting she forgot to write it in her book. That may not sound like an "apology" to you, but she didn't deny she made that mistake; she owned her error, just perhaps not in the fashion you would like her to.

The other issue is your reaction/response/interpretation of what her actions meant which, as you say, could very well be a product of old patterns and behaviors that might be destructive for you.

Your agenda was to get an apology. Her agenda was to have you see that your interpretation of her motivations, etc. was perhaps inflated or skewed by old habits of thinking.

You are not seeing her ownership of her error as an apology. She is not seeing your need for a different kind of apology.

She is wanting you to make the choice to interpret her actions more based on reality than old habits of thinking. You are not seeing her input as focused on your therapy and growth.

Sounds like the responsibility for this impasse is about 50/50 (as impasses tend to be). You certainly are within your right to change therapists based on the scheduling issues. She is certainly within her right as a therapist to try to help you recognize the choices you make (although probably very unconsciously as these types of ingrained choices/habits are wont to be).