Imagine you ask the same question twice to a LLM. Due to the randomness of the replies, it gives you a correct answer and a wrong answer.
If you ask an unrelated question in the same thread, isn't it more likely to give a wrong answer in the case where it already gave a wrong answer for the first question? This is because someone who gave a wrong answer once is more likely to give a wrong answer again, and LLMs mostly predict text.
If that is the case, would telling the LLM that it made a mistake make it more likely to give another wrong answer for an unrelated question, compared to not acknowledging anything? This is because it might "confirm" the idea that the role the LLM is "playing" is of someone who gives bad answers.