The shortest, most ELI5 answer is that, although air is *mostly* transparent, it also has a slight blue-violet color.
We call something transparent if light passes through it rather than being reflected or absorbed on contact. But transparent materials aren’t *perfect* at letting light through without interaction. Even a crystal clear pane of glass will scatter some tiny amount of the light that passes through, you just need a good amount of glass for that effect to be noticeable. A thick enough block of glass will be cloudy white because of this — or with older glass that is less pure likely have a slight green color to it. Even thicker, and it will eventually be opaque.
It’s the same principle, but air is much more transparent than glass. You have to look through *miles and miles* of air before you start to notice the blueish color. On Earth, the distance we can see is limited by the horizon, and usually something is in the way before that. Mountains are huge though, so you can see them at distances where even skyscrapers would be well below the horizon. At that distance, you start to see the hazy blue-violet of the air between you and the mountains. When you look straight up on a sunny day, you’re looking through ~60 miles of atmosphere, which is why it appears to be solid blue and opaque enough that you can’t see the stars on the other side.
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