However, they will most certainly help you change the way you think about that mistake. Which can be extremely helpful in moving past those mistakes and making the best of where you find yourself now in life.
I just recently started seeing a therapist, and this was a huge revelation to me. More specifically, helping me realize I was holding onto a lot of guilt over things where it made no sense to cling to that guilt. Learning to let go of that mental overhead has been extremely helpful.
Well, OK - that realization didn't make my problems go away, but it did set me down a path.
As others have already said, the role of a therapist isn't to solve those problems you have in your life. They might be able to help you not get mentally affected by those problems, though.
When I found out my insurance included therapy, I said "Heck, why not?" Had only 3 sessions with him. The outcome?
I learned that my problems are not severe enough to warrant serious therapy (based on a heuristic they use). That's not to say I shouldn't feel bad about them or anything, but to highlight that yes, people have ups and downs, and I may have just a few more downs than the median, but I'm not far from the median.
The problems I was dealing with had solutions. He outlined a few options to me and recommended some books. I picked one of the options and started reading those books (frankly, I was interested in the topic anyway).
Knowing that my problems were ultimately due to the lack of a few (learnable) skills makes a big difference. And now I can see people around me who have similar issues - some who think they've got serious psychological problems - and their internal mental torment is rather sad.
Agree with what others have said: Plenty of crappy therapists out there. I seem to have been lucky with mine.
Rather therapists help you not make the same mistake again.
A lot of humans think "But I'll never make that mistake again!"
But then they do. We're just not evolved to live in modern environments, so our brains and nervous systems lead us to do silly things.
Therapists help reduce the likelihood that you keep making the same mistakes. And they provide techniques to mitigate the risks arising from new types of mistakes you might make.
It's why our sessions all focus on brief therapy and practical psychology principles.