LLMs are a superintelligent rubber duck.
"Rubber ducking" is the phenomenon where when faced with a programming bug, and explaining it to another person (who is just nodding along, like a rubber duck) you solve the problem yourself.
In explaining it to someone else for them to understand, you had to explain it to a level where the problem pops out to you, too.
You were missing the problem before because in your mind you were skipping over an important detail with a hand wave, but trying to explain it to someone else required you to engage with that detail and thus discover the problem.
LLMs are a great conversation partner for you to figure out the answer yourself.