I explained this as: Take a number, e.g. 5. Then take a small number, like 0.1. Add 0.1 to itself, and repeat, you'll eventually reach 5.

But if you take 0, and keep adding 0 to it, you'll never reach 5. So no amount of 0's will go in to 5.

That logic breaks down if you do 0/0 though. My students never picked up on that one but they believed me!