Before we can answer why milk is white, we need to explain why anything at all appears white. It is just a matter of simple physics. The reason why items appear white is because they reflect all light wavelengths and absorb none. If all wavelengths of light were absorbed and not were reflected back, the object would appear black.
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While milk is primarily composed of water (approx 87%), which is a colourless liquid; there are other components of milk (fat, protein, lactose, minerals and vitamins) that influence the colour of milk. The fat and protein molecules in the milk reflect light at a wavelength that makes the liquid appear white.
If we were to remove some of the fat from the milk (like in skim milk), it would give the milk a different colour because of the wavelengths the light is reflecting back to our eyes. That is why skim milk has a bluish tinge.