"If you went to a dentist and felt they were not competent you would go to another one. You wouldnt traduce the whole profession." @MrsChristmasHasResigned
I think the difference is that if you go to a dentist over a toothache, they'll take an x-ray and tell you (for example) that you have a cavity, and 99% of the time they'll do a perfectly good job filling said cavity, fixing the problem. You have a problem, there is an established guaranteed solution, and they will enact it. If they don't do so successfully, you can complain and have that remedied.
With therapy, however, even with qualified clinical psychologists, there is no one way of doing things - there are a variety of different types of therapy (DBT, CBT, EMDR etc) which may, or may not work, on certain types of people or trauma, and which may, or may not, be enacted well by the psychologist. Methods and efficacy vary wildly, and every time a person tries a (private) clinical psychologist, it costs them a large sum of money per session.
A person could go to a psychologist for multiple sessions, trusting that it takes time to see the effects, only to discover that they never progress anywhere because the type of therapy isn't appropriate for them/their type of trauma, or the psychologist just isn't the right fit for them. But of course, that money and emotional energy has been wasted - and it's possible the person may be blamed by the psychologist for not making progress.
It makes therapy feel like a gamble, because ultimately it is, and that makes people justifiably suspicious.