How can I explain alien skin being different colors?

In humans skin color varies slightly in shades of dark brown to a faded pink, which has the purpose of protecting the skin from sunlight. An idea used commonly by people beginning designing alien is to have their aliens have every possible color of skin under the sun, but in my mind this is kind of unlikely.

How can I explain why a species would have every possible skin color under the sun? Why would a race of species have orange as a skin color? What about red? Violet, Blue, Green, Yellow, etc?

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How can I explain alien skin being different colors?

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