Q. Why don't we see air?

A. In fact, we do see air all the time - in at least two different ways:

1) When you look at the sky, you see the blue color of air - this is caused by the air preferentially scattering light of shorter wavelengths - blue being the shortest. All air is blue (but only a very, very, faint blue) because of this scattered light - just as a red rose is red because it scatters red light preferentially. however, due tothe very faint nature of this color, it is only readily visible when you through a lot of air at once - like in the sky. On very clear days you might notice distant mountains aquire a blue shade, due to the blue air between you and them. You can investigate this further with an experiment.

2) We can also see air's effect on the path of light. Through the phenomena known as refraction, air bends light. This is most visible when a layer of hot air sits next to a layer of cool air (the temperature of air has a strong effect ont he refraction) - the light can be strongly bent forming mirages. Although mirages are usually associated with the desert, if you've ever driven on a hot da, you might have seen them looking like puddles in the road that vanish as you approach. In this case, light is so strongly bent as it goes from the cool air to the hot air directly above the road that it reflects upwards at you like it would off the top of a pool of water. Your brain is more used to pools of water than it is to refraction, so it thinks it is seeing a pool of water.