White paint can’t be made from a mix of other colours because every other colour absorbs some of at least one wavelength. Subtractive colour mixing is the process of mixing paints or filters together to make new colours.
For example, cyan paint absorbs some red light, no matter what shade it is. Some blue light is taken in by yellow paint. When you mix these colours together, you get a green colour because the mixture absorbs some of both the red and blue wavelengths. Some green light is absorbed by magenta pigments, so when you mix equal amounts of equally bright cyan, yellow, and magenta paint, you get grey. Even if all three pigments are very light colours, the result can only be a very light grey because not all wavelengths are reflected instead of absorbed. So, the only way to make white paint that looks white to the human eye is to use a single compound that reflects red, green, and blue light.
But the opposite is true for additive colour mixing, in which wavelengths are sent out instead of taken in. If a red, green, and blue spotlight all point to the same place, the result is white. This is how TVs, fluorescent lights, and computer monitors all work.