Well, we can only see a tiny bit of the available light hitting us all the time - from 400 to about 800 nm wavelength. I guess it would be unlikely that a random chemical would be able to interact with light in a selective way.
It's much more likely that the chemical has no particular interaction with light which discriminates between any of the range 400-800nm; so most chemicals just reflect all light equally, so are white.
It's sort of like asking the question, why do most things in the universe not resemble a letter of the english alphabet? Because english letters are only a tiny fraction of all shapes.
But that's not the real answer to the question, which is really how do molecules somehow reflect only a certain wavelength of light? i.e. what types of physical properties make a molecule respond differently to only slight differences in the wavelength of light? Is there only one particular shape, which can be bent or modified in various ways, and each modification changes light in a different way?
i.e. there would be a molecule with a bend in it, and if the bend is between 20 and 40 degrees, it interacts with light. 20 degrees knocks out red light, 21 degrees knocks out a different set, etc. Or it could be the case that there are many types of molecule which interact with light.