After class, a fellow student whom I'll call M brought Professor Loomis a proof that M knew was incorrect. A group of us students gathered round to help Loomis find the flaw in the proof. Every step was intuitively correct, but it led to an incorrect conclusion. How intriguing! Did this reveal a fundamental flaw in the fabric of the universe? Of course not. But what was wrong with M's proof?
There were a dozen or so simple steps, and for each one, I knew an airtight justification for why it was true. Each one, except for one that clearly had the ring of truth.
I pointed to that step and said "I don't understand why this is true." The other students chimed in to explain it to me. (Some people now call this "mansplaining".)
Loomis exclaimed, "That's it! She's got it!" I felt like Eliza Doolittle with Henry Higgins, and wondered if we should burst into song. I fell head over heels in love with him.
Loomis gave us a counterexample for that step. I wish I had thought to do that! I hadn't thought any further ahead than "I don't understand why this is true."