First we have to understand their definitions.
Mixture: a substance made by mixing other substances together physically.
Compound: made up or consisting of several parts or elements chemically.
Now that we understand their definitions we can justify and clarify that air is a mixture.
The air is composed of many non-reactive gases such as nitrogen, hydrogen, methane, water vapor, carbon dioxide, etc. It can not be classified as a compound because compound means; several things (elements) compose a whole but chemically, and this previously mentioned gases are attached physically, not chemically.