I've come to think that if someone can't explain something well, they probably don't understand it as well as they think. I've heard people that fancy themselves experts on this or that software concept, and when trying to explain it use all the technical jargon they possibly can. It comes off as just regurgitating things they've heard before.

In other words, I suspect the scientists that couldn't explain p-values in an intuitive way, didn't themselves fully grasp the subtleties of p-values.