As a teacher, I see this debate a lot.
I believe the original quote about those who can, do, and those who can't, teach is attributed to George Bernard Shaw.
The first time I saw that quote was when, coincidentally, I began teaching. I was offended. But I was also curious. What exactly does that mean?
On the surface it suggests that if you're good enough to do something (say, throw a football accurately), then you do that and make a living. But once you're "washed up" or if you were never quite good enough to make it, then you teach it to beginners, since you know a lot about it or were once able to do it.
But that kind of thinking is very simplistic and isn't productive.
Teaching is a skill, and a bit of an art form, that requires a mastery of teaching. It really requires an understanding of how people think and how to motivate people.
Take golf or acting, for example. The top-level pros still engage in hiring coaches. Why? If we go by Shaw's assumption that a top golfer has nothing to learn from a golf coach, then why do all top-level professionals seek coaching?
It's because coaching is a separate skill set.
Think of it another way. I'm an excellent driver. My clean record goes back to 1994. I look both ways twice, actually follow all the rules of the road, and don't speed. But I do not like teaching my daughters how to drive. I'm not patient enough with them and, frankly, find it quite frightening. It's incredibly stressful for me.
Hiring someone who teaches it professionally is worth it. That person knows what he or she is doing. And they took courses themselves in how to teach it.
Finally, I teach engineering and technology to middle school students. I used to teach reading to elementary school students. I don't need to be an engineer or a professional reader (I suppose there is such a thing) to be able to teach it. I need to understand how the tween and teen mind thinks. I need to be able to manage 25-30 different personalities, help them focus, work, cooperate, and appreciate the subject. I also need to help them succeed.
Could a real engineer come in and teach these classes? Maybe. But I've had a lot of guest speakers and demonstrators over the years, and I can tell in the first five minutes of the lesson if it is going to head south. And when it does I have to try to patch it up in a way that helps the guest save face. Not easy. Sometimes they have no idea what they are doing, so the fact that they are excellent engineers doesn't matter if they can't keep the attention of a room full of teenagers.
About qualifications: Even if someone is the greatest photographer in the world, he or she needs training in how to teach and guided practice in teaching others. The degrees required to be a teacher or professor are also there to make sure that the teacher or professor is serious and dedicated, long term, to the career of teaching. It's a proving ground in a sense.
That said, another hallmark of a great teacher is one who brings in the pros to help the students see the real world connections and to hear the anecdotal aspects of the career.
In conclusion, there are many teachers that CAN do but choose not to because they actually find teaching to be more fulfilling or stable. Many acting coaches come to mind. They don't participate on stage or on film because they don't want to.
A great example is Ron Howard. He would rather direct the actors than act. We all know he can act, but that's not what he wants to do.