How to explain why aluminum won't work on an induction stove?
A induction stove is a high frequency transformer. The primary winding is built into the stove, the secondary winding is the bottom of the pot or pan placed on it.

In principle, such a transformer works with all types of conductors as the secondary. The problem is, you want to have a high electric resistance in the secondary. Because that high electric resistance is what produces the heat inside the bottom of the pot or pan.

And here's where aluminum and copper drop out. They are good conductors and have a low electric resistance.

Iron in contrary has a very high electric resistance because of one special feature: because it's ferromagnetic AC currents can only flow in a very thin layer below its surface. This is called the skin effect. Again, every metal shows that skin effect, but for iron it's 80 times higher than for aluminium and copper. And so is resistance and heat production.

That's why you need an iron sheet in the bottom of your pot or pan.