Is that true though? How do we know that the ability to teach is not a unique skill in and of itself rather than just an extension of one's "mastery"?
Anecdotally, I've engaged with "masters" of various fields as different as blacksmithing to theoretical physics. Of these "masters", I've encountered good teachers and bad. But I've not personally felt any correlation between their mastery of the subject (i.e. their ability to produce results in the area) vs. their ability to teach the area.
I've had various trainers in boxing. Most of them were damn good boxers. One of the best was a real talent, been boxing since he was 10. He never went very far with competing, but ho boy did he look great at the gym.
When explaining how to do something, he really struggled. Most of the time he could show us what he does, but not explain how he does it, why he does it, or sometimes not even realize what exactly he does until he tries it. Then he's like "Oh yeah I guess I do take a little step there, you're right"
Then there's a trainer who is a little less talented himself, competed at a pretty decent level as an adult, but decided to pursue training instead. He can tell us what to do and why we should do it. Also how to think about strategies and whatnot. He's great but we need a lot of repetition and trial and error.
Then there was the lady who is an 8 time professional world champion on Muy Thai. She came to our gym to become a better boxer and to get free membership she offered to teach.
Dude, that was on another level. She could not only explain why we should do something, but also how. She'd look at your punch and be like "No no, move your wrist 5 degrees this way" and damn did it immediately make an impact.
3 months of working with her created more boxing improvement than 3+ years of other trainers has. It was phenomenal.
The difference was that she wasn't just talented, she also had a deep understanding of exactly what you have to do, why you have to do it, and how you have to do it. Her advice was measured in half-inch adjustments to your technique.
Teaching might be a separate skill, but true mastery is being able to break down exactly how you do what you do and why.
Oh and better yet: she explained how it should feel when we get it right. So not only would we know what to do, but also how to tell if we did it right.
I also have taught English to novice speakers and sometimes am struck by such questions they receive, sometimes being all of: obtuse, irrelevant and pedantic at the same time. But that is their primary objective: to sell tests and teaching materials to their tests, not direct competency.
But teaching isn't simply being able to explain why something is the way it is. It's more than that.
I could explain to you why planets move the way they do by using the language of tensor fields built up out of tensor products mapping vectors to their duals. It would be a thoroughly accurate definition of why we see the movement we see but it would not necessarily be a good way to teach. Particularly if the recipient of the teaching wasn't familiar with the formalism of general relativity.
It's this aspect, that teaching is more than simply understanding that makes me think it potentially could be orthogonal to mastery of a subject.