Shouldn't the end product of a system with such symmetry be more randomized than the initial?
Aerrodynamics is a complicated subject! I believe the answer to your question is because the exhaust air has been concentrated into a fairly constrained channel by the shape of the fan's blades, at least close to the blades where you're most likely to put your hand to feel it. But the air being drawn in from the back of the fan comes from a much larger volume, and therefore the same mass of air can move with a lower velocity.
In short, the fan isn't a very symmetrical system.
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