First, experienced people often develop mistaken beliefs. They try something and it happens to work, even though it might even be wrong in principle. Without any rationale, how is the person you're talking to going to judge whether the beliefs you've developed are correct?
Second, even if they're willing to trust you, just getting the rule handed down does not grow them as an engineer. I might prefer to make a mistake and learn than take the right path without understanding the reasons. In fact, I have done so, intentionally.
So, again, IMO, the goal you've mentioned in this comment ("figure out how to tell them `trust me...`") is an incorrect goal, and one you should not pursue.
You could ask questions that lead them to the same conclusion (with the benefit of hindsight from your experience): "What happens if this system is terminated before the final write call completes?" "How does this handle someone accidentally starting another instance of the application at the same time?" "If this external service we use is down, what happens?"
You could also walk through the story of your prior mistake, draw parallels to the new code, and then discuss how to avoid it.