I used to pride myself on the fact that I could explain almost anything to anyone, on a simple enough level, using analogies. No matter how abstract an idea in physics may be, there always seems to be some way in which we can get at least some part of the idea across. If colleagues shrugged and said, oh, well, that idea is too complicated or too abstract to be explained in simple terms, I thought they were either lazy or not very skilled in thinking creatively around a problem. I could not imagine a form of knowledge that could not be communicated in some limited but valid approximation or other.
However, I've changed my mind, in what was for me a rather unexpected way. I still think I was right in thinking that any type of insight can be summarized to some degree, in what is clearly a correct first approximation when judged by someone who shares in the insight. For a long time my mistake was that I had not realized how totally wrong this first approximation can come across for someone who does not share the original insight.
Quantum mechanics offers a striking example. When someone hears that there is a limit on how accurately you can simultaneously measure various properties of an object, it is tempting to think that the limitations lie in the measuring procedure, and that the object itself somehow can be held to have exact values for each of those properties, even if they cannot be measured. Surprisingly, that interpretation is wrong: John Bell showed that such a 'hidden variables' picture is actually in clear disagreement with quantum mechanics. An initial attempt at explaining the measurement problem in quantum mechanics can be more misleading than not saying anything at all.
So for each insight there is at least some explanation possible, but the same explanation may then be given for radically different insights. There is nothing that cannot be explained, but there are wrong insights that can lead to explanations that are identical to the explanation for a correct but rather subtle insight.