“Why do complementary colors desaturate each other?”
A mix of two complimentary colors is less saturated, because complimentary colors are composed of wavelengths that trigger different cones in our eyes. When combined, all cones are triggered more evenly, which makes our brain perceive the result as less saturated.
First, I think it’s important to keep in mind that “color” is a human construct to describe things we see - it makes color theory easier to understand. Colors are not consistent across languages (although there is some logic to them), some “colors” (e.g. silver vs blue) describe different optical qualities, and so on.
So, what are colors? Everything we see is because of light. Light comes into our eyes and hits photosensitive cells, and some of these cells are sensitive to different wavelengths. Most people have three types (some have less, some have more). Our brains perceive these three signals as colors: blue (shortest), green (middle) and red (longest). (more info)
When all types of cones are stimulated evenly, we see white (or grey, depending on the amount of light).
“saturation” is one of the terms we’ve created for describing colors. Saturation describes how “bright” a color is, or from the other end, how far from white it is. Therefore, we can roughly say that a saturated color hits only one or two types of cone, while desaturated hits all types to some degree.
The color wheel
So, how does one take wavelengths and eye cones and get a circle? The color wheel is a tool created by painters to predict how will different colors behave when mixed together. We figured the wave stuff after we made the wheel. The fact that the new science didn’t break it is a testament to artists being really damn good at observing and describing cause-effect relationships.
So, in a way, we can say that we call colors “complimentary” because they desaturate each other. They’re on the opposite side of the color wheel, because that’s what makes the wheel work as a predictor.
So, why do complimentary colors compliment each other? It’s because they consist of wavelengths that trigger the other cone types. If one color triggers one cone type, the other triggers the other two. When you put complimentary colors together, the cone types are triggered more evenly, which makes them look closer to white, therefore less saturated.