>No matter how knowledgeable a teacher is, how well they convey that knowledge, and how well the student comprehends it, there is always more on that subject to learn.
This. I have a couple of anecdotes, not that anyone asked. First, on the student side.
I taught Western Civ for many years. One standard lecture was about Athenian democracy, of course, and how very different it was from modern ideas about democracy. This usually went well. From the teacher's point of view, I can read student faces, see them taking notes (this was before mobile computing). I could see comprehension dawn.
Then, one fine day, a student came up after class to ask a question. From the way it was phrased, I realized this student had completely misunderstood what I had to say. And now comprehension dawned on my own face, for I realized that there was no way for me to know whether those looks were ones of understanding or of understanding wrongly. It was one of several factors that helped me understand the limitations of live teaching.
The second story comes from the teacher side. I started teaching online very early (1994) and by the late 1990s had full courses online, with my lectures turned into essays. They were once very popular across the Internet, some of them appearing consistently on the initial page of Altavista and then Google. So they got seen widely. Every once in a while I'd get a nice note from someone pointing out that I'd got something wrong. Very occasionally this was just a typo, but more often (not frequent--once every year or two) it was a factual mistake. I was still close enough to my grad student years that I knew the information had come straight from my own classroom notes, or from reading.
In other words, it was something I knew as true, but I was wrong. But I'd been teaching that bit of information for years. Hundreds of students had dutifully written down the wrong thing. And promptly forgotten it, but never mind that. This realization was another factor in moving me toward teaching online exclusively; for, in the live environment, I very probably never would have been corrected. Putting my teaching out where the general public could see it made a big difference. Sort of like publishing your novel instead of just having your friends read it.
Anyway, both anecdotes illustrate concretely the statement made by - K2 -.