If you can't explain it simply, you don't understand it well enough.
There is some truth to that, but some things are legitimately complex, and while you can give a simplified version to a layperson, you'll never be able to give them a full understanding. You might not even be able to give them a sufficient understanding.
Disclaimer: I'm no great physicist, so the physics details in this post might be off. They're besides my point.
Ultimately, when you're working with a simplified version of the truth, there's a lot of room for misunderstanding, not to mention doubt on the listener's part. You can say something like:
"The radiation coming from your phone isn't the kind of radiation that causes cancer".
This is true, and easy to understand, but what does the listener really learn from this? It's just a statement to them, something they can either choose to believe or not. You can add some minor details, to give them a slightly better understanding:
"The radiation coming from your phone has a completely different wavelength from, for example, X-rays or gamma rays, and consequently the energy they contain isn't high enough to cause damage to your cells".
Now they know a little bit more, and might have more reason to believe you. Still, they don't know where this knowledge comes from, nor do they really know anything about the interaction between EM waves and DNA. They might not even really know what DNA is, not to mention EM waves.
Okay, you can then give a simple explanation for each of those things, but the more things you need to explain, the more difficult it becomes to understand, and the room for doubt increases.
I'm an electronics engineer, working with computers. I understand computers quite well. However, when my mom asks me to explain how they work, I always end up hitting a wall at some point. I can give her a simplified version of everything, and she may understands each point, but by the end she can't remember enough about each point to understand the whole. It's simply beyond her grasp, and she's not stupid. She just has no understanding of technology. The best I can do in the end is say something like "Computers are a bunch of circuits which process numbers," but she pretty much already knows that, and her understanding doesn't really improve by much. What can I do then?
EDIT: Just thought of a classic example of this, from Richard Feynman (which I'm sure many of you have already seen):
I bet Feynman understood magnetism, he still couldn't give a simple explanation which feels satisfactory to a layperson.