Paraphrasing from How to Take Smart Notes by Sönke Ahrens: we easily get away with unfounded claims when we speak orally. We can distract from argumentative gaps with a "you know what I mean", even if on introspection we would find that we don't know what we mean. Writing permanent notes will make these gaps obvious.
I often make mistakes when solving math problems without due care, whether by skipping too many steps, moving to quickly, or failing to check my work. I am aware of the weaknesses in the human mind when solving logical problems and take steps to mitigate them. By the very nature of math problems, I know when I get a wrong answer. Even if the value of a calculation is unknown, I can still check each logical step and know when I have erred. Yet when reasoning verbally, I don't get this feedback. Even if I have made several complicated steps in an argument, I may feel confident in my conclusions and most of my deeply held positions have never been subject to the scrutiny of being worked out on paper and verified step-by-step. Yet, I know that this is what it takes to really be certain of a mathematical argument and I would never be confident in my solution to a hard math problem that I had not checked. I temporarily forget my own weaknesses when verbalizing an argument.
An extension of this idea is that most people consider themselves worse at math than at reasoning through words, but I think this is misguided -- this is just over confidence due to lack of feedback when one is wrong. A counterpoint is that perhaps humans actually are better at verbal reasoning than mathematical reasoning and so it is reasonable to have more confidence in your verbal abilities. I doubt this is true and if anything the unquantified language we use when dealing with ordinary issues seems more fallible to me. Anecdotally, I have found fatal flaws in my own arguments once I take the time to write them down.
Remember your weaknesses and don't forget to check your work.