I have no educational background in psychology, just a casual curiosity. Do therapists need therapy because it’s impossible for people to see their own blind-spots (I think this is called the shadow)? Are there ways you can train people to see weird distortions in their own logic on their own, or do they always need an outside party?
As pointed out in another answer of mine, therapists are not immune to psychological problems. In fact, one study shows the lifetime rate of depression in psychologists and social workers to be higher than that of the general population (Deutsch, 1985).
They hear about difficult, sometimes traumatic experiences as their clients share their issues. This can lead to problems due to the phenomenon known as Emotion Contagion. They too occasionally have personal problems and things they may find difficult work through without some assistance. See This TalkSpace article for some other examples of how therapists might need therapy.
As you indicated in your question, sometimes this may not be immediately noticed by the therapist for reasons like hidden issues. As I have pointed out in another previous answer - see for more info., there is Clinical Supervision which helps to highlight any possible psychological issues or hidden traits — e.g. prejudices or other incorrect thought patterns/conclusions) — which may need therapy (See my answer talking about Johari Windows for more on that). This is standard practice, and required in codes of practice for registered counsellors, psychotherapists, psychologists, psychiatrists, etc. and those in training.
Deutsch, C. J. (1985). A survey of therapists' personal problems and treatment. Professional Psychology: Research and Practice, 16(2), 305–315. https://doi.org/10.1037/0735-7028.16.2.305