Why does FM sound better than AM?

Someone gave me an analogy some time ago that made a lot of sense.

If you shine a flashlight through a tree blowing in the wind and vary the brightness to convey information, the signal can get distorted pretty easily.

However, if you have a constant brightness source and vary the color, it’s a lot easier to figure out what the source is trying to convey.

I always shy away from analogies because more often than not they give the wrong "feel" for a concept. But this is one of those rare exceptions.

It _is_ the wrong feel for a concept. The analogy breaks down because the color changes are way too wide in frequency (and thus too robust to noise) compared to what happens in a radio broadcast. If you changed the color from RGB(127, 0, 0) to RGB(126.999999, 0.000001, 0), the movement of that tree would actually start to make your strategy difficult.

Going from red to orange is about 50 THz. Typical FM radio modulation width is 100 kHz.

The analogy isn't wrong, it's just that it is incomplete as given. You are bringing the sensitivity of the receiver into the equation. But it doesn't really break down the analogy, because the frequency shift in color is calibrated for the human eye's sensitivity. Calibrate it for a FM receiver and that tiny color shift becomes easily discernible. The tree leaves have no impact on frequency, just amplitude.

The reason the analogy is good is because it isn't even really an analogy, it is in fact a description of electromagnetic waves and a noise source.