Why is the sky blue?

Because air molecules scatter blue light far more strongly than red. This is Rayleigh scattering, and its strength goes as the inverse fourth power of the wavelength — the shorter the wavelength, the more it scatters.

Blue light has roughly half the wavelength of red. Raised to the fourth power that difference becomes enormous — blue scatters about ten times as much as red. So blue light from the sun arrives at your eye from every direction in the sky at once, and you see blue everywhere without looking at the sun itself.

Violet has an even shorter wavelength, so why is the sky not violet? Two reasons: sunlight contains less violet than blue to begin with, and the human retina is far less sensitive to violet. Together they settle the result at blue.

The same physics reddens sunrise and sunset. The light then crosses a much thicker slab of atmosphere, nearly all the blue is scattered away en route, and what survives to reach you is red and orange.