As a t in training, a big part of this is how and when to terminate. At T's and clients are all (mostly) human, there will always, always be instances of a 'bad fit', often no more than a personality clash, or a client needing a different treatment modality than that offered by the t.
As with anyone who provides a service, this is part of the job. I guess that all driving instructors, music teachers, personal trainers etc etc have had clients move on, or have had to finish with clients. There are training books on how to best manage a termination, but often it happens very suddenly, so there is not good time for closure.
I think it's so important to remember that T's are human beings, doing a job, probably because they like the work, and they care about their clients, but also for the same reasons that everyone else gets up and goes to work each day. And yes, failing is hard because it affects another, potentially vulnerable, person, but it's inevitable sometimes.