Advantage of zero knowledge protocols
Here's the example I use sometimes.

Suppose I want to convince you that I am an excellent archer.
If I show you a target painted on a wall, and an arrow in the bullseye of the target, are you convinced? No, since for all you know I could have fired the arrow first and then painted the target around it. In fact, even you could have done that, and you not a skilled archer. If instead you yourself paint the target first and watch me fire the arrow at the bullseye later, that's much more convincing.

So the "byproducts" of this interaction (the target and arrow) by themselves are not convincing. You could have generated them yourself (i.e., simulated them) even if you are an unskilled archer. Only if these byproducts were generated in a particular interactive way do they become convincing.