(((Okie))) first of all, there is no such thing as "dumping" a patient, not among real therapists. We refer them, or terminate therapy. Not that that sounds any better.)

Even if it becomes all about the therapist (as in they are triggered, afraid of, have medical issues or for any reason are unable to professionally treat the disorder, etc) they make sure it doesn't inflict damage upon the patient. Changing doctors can be tough, sure, but there are professional, ethical ways to do it.

From the APA guidelines:

10.10 Terminating Therapy
(a) Psychologists terminate therapy when it becomes reasonably clear that the client/patient no longer needs the service, is not likely to benefit, or is being harmed by continued service.

(b) Psychologists may terminate therapy when threatened or otherwise endangered by the client/patient or another person with whom the client/patient has a relationship.

[b](c) Except where precluded by the actions of clients/patients or third-party payors, prior to termination psychologists provide pretermination counseling and suggest alternative service providers as appropriate.