I think the geometrical explanations aren’t correct, even if they feel satisfying.
The answer has to do with the Reynolds number and inertial versus viscous behaviors of the air.
If you ran the fan slowly enough, the flow pattern would become symmetrical front and back. Actually, for a propeller fan, the flow would become entirely rotational, with no travel along the axis, so maybe bad example, But if you had a magic grill that sent air perpendicularly through, and ran that slowly enough, there’d be symmetrical flow patterns.
Somewhere on the web is an interesting discussion of the Reynolds number that reveals that animals with a single degree of freedom in movement, such as clams, could not locomote themselves at all in a low Reynolds number environment.
So, the flow is more directed in front of the fan because air leaving the front has all its momentum directed in the same direction. If you put a diffuser grill on the front of the fan that reproduced the directional pattern of the back, you’d create a symmetrical flow system that way too.