Air generally gets moving because of pressure differences. As an example, when you blow air out of your mouth, you use your diaphragm to squeeze your lungs and raise the pressure of the air in them a little, and it flows to a region of lower pressure in the room.
You're right that it's possible to get air moving by friction. If you move a piece of cardboard through the air, with it oriented for least resistance (aligned with the movement), some air will be dragged along with it by friction. But if you turn it sideways so it's oriented like a paddle, it will create a high pressure region in front of it and a low pressure region behind it, both tending to get air flowing in its direction of movement, and it will move a lot more air.
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