Being a therapist calls for much more clarity, honesty, and authenticity than being a trainer, hairdresser, even a GP.
There are many reasons why I might need/want to stop working with a client, most of which would be quite straightforward to talk about (logistical/scheduling issues, realising that we have a mutual friend, me recognising that the client would better be served by a specialist therapist etc).
Rarely it might be a difficult thing to discuss, either to do with some process that's more personal to me (eg overwhelmingly positive or negative feelings towards them that I can't work through with my supervisor and/or therapist, such as they have a haircut that reminds me of my god awful uncle Bob and I just can't get past it - this is a jokey example). Or it might be something that is more to do with them (they become physically threatening, they have a persistent misperception of what therapy is about).
I would never fudge the ending of our therapy by pretending that I wasn't available. This would do them a grave disservice, and is so disrespectful. I would be as honest as possible without burdening them with my own personal stuff (uncle Bob's haircut). Most people are quite intuitive and will have an inkling if they're being fobbed off, and it's straight up unethical to "gaslight" them into ignoring their intuition.
Remember that many people coming to therapy have had some sort of difficult or even abusive relationships, in which they've been rejected, lied to, shamed for being needy (as a child) etc. It's incredibly important as a therapist to offer an authentic, well-intentioned relationship that helps then rebuild their trust in their own wisdom/intuition and sense of worth.
I should also add that the onus is on me as a therapist to try and work with clients I don't "like", and to work through their "dislikeable" ways of being with them. A good therapist shouldn't cherry-pick the "nice" clients and drop the tricky ones. So in that sense it's also different from being a trainer, hairdresser etc where there's no obligation to work with someone "dislikeable".
I've come back to this thread to reiterate all this because I want to challenge some of the mistaken beliefs about therapy. If I was thinking about starting therapy, I'd be pretty put off by lots of the comments!