I agree with parts of all the replies to OP but overall I think that the expectation that we can always discuss what we want /effectively have want we want at the time we want it is unrealistic in all areas of life and this includes when we are paying another human being to "hear"us
Training and experience should prevent professional persons from letting their emotions get the better of them however difficult the situation presented but it's impossible to be 100 percent all the time and I'd prefer someone admitted they can't talk to me at this time than say something that may be impossible to come back from-I think this shows respect for both parties-for myself as a veterinary surgeon I deal with a huge range of emotions in clients from the pain of euthanasia to the joy of a new puppy to anger over cost/failure of treatment etc in the space of 10 minutes-I've never lost control of my emotions but like the therapist being discussed I have known when I need to step away(in my head -not literally)
I know the pain of waiting for a therapist to respond/reschedule /be more empathic/more understanding etc but to then berate one who admits they're struggling and need some time seems to be a no win situation for the therapist