Hated "showing my work". If I knew the answer because my brain calculated it, why do I have to 'show it'. I did not always know what 'to show'.
The way I understood it there were two big reasons to show your work:
1. To prove you were not cheating.
2. To get any partial credit if you just didn't do the arithmetic part correctly (for math, physics).
But a big part of it really is because a lot of people see/know the answer but not how to get the answer. And the point of the problem is to learn HOW to get the answer. Making someone go back and write out the steps helps solidify and clarify the process and also shows both the problem solver and the person grading the problem any weak or misunderstood or missing parts of the understanding.
I would never have really 'gotten' that part if I hadn't had to insist one of my kids write out the steps to solve the problem. Like many smart people, the answer was 'obvious' but he didn't really always understand or understand as well as he thought he did WHY that was the correct answer. And if you don't know the whys and hows and all the steps, the more complex problems will be more difficult to solve. A lot of smart people get somewhere into college before reaching that point but if you do get to college without ever having had to study or work to know what the answer is, eventually, you WILL get there and you will lack the skills and confidence to solve the problem efficiently and correctly. If not college, then grad school or real life. So far, I haven't met anyone who hasn't hit the wall at some point, including some exceptionally bright people.