Why is the sky blue but sunsets red?

Both phenomena come from the same process, called scattering, and understanding one explains the other. Sunlight contains all colors, and as it passes through the atmosphere, the tiny molecules of air scatter it, deflecting it in all directions. Crucially, they scatter shorter wavelengths (blue and violet) much more strongly than longer ones (red and orange), an effect called Rayleigh scattering. During the day, when the sun is high, sunlight passes through a relatively thin slice of atmosphere, and the blue light gets scattered all across the sky in every direction. So when you look up, you see that scattered blue light coming from all over the sky, which is why the daytime sky is blue. (It scatters violet even more, but our eyes are less sensitive to violet and some is absorbed, so we perceive blue.)

At sunrise and sunset, the geometry changes and so does the color. When the sun is low on the horizon, its light has to travel through a much longer, thicker path of atmosphere to reach you, angling through the air sideways rather than straight down. Over that long journey, nearly all the blue light gets scattered away out of your line of sight, removed before it reaches you. What is left to travel straight through to your eyes are the longer wavelengths that scatter least, the reds, oranges, and yellows, which is why the sun and the sky around it glow in warm colors at dawn and dusk. Particles and pollution in the air can enhance this, sometimes producing especially vivid red sunsets, which is why dramatic sunsets often follow certain weather or after events that put more particles in the atmosphere. So it is one mechanism with two faces: air scatters blue light most, which paints the overhead sky blue by day, and strips the blue out of the long slanted sunset light, leaving the reds to color the horizon at the beginning and end of each day.