"... then you haven't understood it."
We all have heard variations of that. The idea here is that if you understood something, then you should be able to explain it in its simplest form to someone who has no background in a certain knowledge to be able to understand it. I've heard this told to physicists, and told by many people who should know better than repeating something unverified.
And that's the whole problem. The statement is mentioned and repeated AS IF IT HAS BEEN VERIFIED TO BE TRUE! So when it is uttered, most of us tend to get defensive and try to deflect it, rather than confront it directly and ask to show proof that the statement is true.
The problem here is that people confuse two things: (i) having knowledge and (ii) the ability to convey that knowledge in simple, understandable form. These two are NOT mutually inclusive! If it is, then someone needs to go out and proclaim that a physicist such as Dirac "doesn't understand quantum mechanics". Anyone who has read his biography could easily see that he wasn't much of an "explainer", and certainly not to the general public. So, who here in his/her right mind would like to proclaim that Dirac doesn't understand quantum mechanics? Anyone? How come this clear and obvious falsification to that statement never brought up? I have plenty more examples from where that came from.
Most of us who have been in physics for any considerable period of time have met people who we KNOW for a fact to be experts in certain areas, and yet, they suck at explaining what they do to us, much less, to someone who isn't familiar with the subject matter. This may happen for a variety of reasons: (i) lack of pedagogical skills (ii) laziness in figuring out how to present something at the level that the audience can understand (iii) or simply a complete ignorance of the fact that the audience is clueless to what he/she is saying. Being able to present something in understandable form is not a skill that comes with knowledge. It requires quite a bit of thought, a consideration to the level of knowledge of the audience, and a lot of consideration on how to present something that is in touch with what the audience already know. This takes effort, and this is something not everyone realizes. Thus, you get brilliant scientists who could have a lot of trouble explaining something that a grandmother can understand. It has no reflection on his knowledge of the subject matter.
A few years ago, while explaining what we do to a group of general public visitors to our facility, one of our distinguished, senior theorist happened to be listening to my spiel. The next day, he walked into my office and told me that, after years of listening to my boss, and the previous boss of the group explained what the group's project is all about, yesterday was the first time he actually understood what we were doing! I was of course flattered, but also a bit shocked, considering that our group has been headed by people who are among the world's leading experts in this area! So to say that these people did not understand what they're doing is utterly false, because I KNOW for a fact that they do. And by that same token, just because I somehow have a bit of a skill in explaining such a thing, does that mean that I've understood it, and understood it more than they do? Nope, and certainly not to the same level as these experts that I look up to.
A lot of crap gets thrown out nowadays and accepted as "fact". The notion that the ability to explain things in simple is somehow commensurate with one's mastery of the subject is patently FALSE. It carries as much validity as claiming that if you can't sing very well the songs you wrote, then you're not a very good songwriter. One has nothing to do with the other!