Most answers about how spinning devices create suction often mention how air moves from high pressure to low pressure. The spinning fan creates low pressure and thus we have air moves from freestream (high pressure) toward the fan (low pressure). My question is: How is the low pressure created?
The pressure difference is created mainly because of the angle of the fan blades. The blades reroute the air molecules creating regions with deficit of air (low pressure). $fig \ 1$ shows the cross section of a fan blade moving with some speed. The same can be visualised as air moving towards the blade with the same speed (on average) as in $fig \ 2$.
Due to the fan blade pushing the molecules down, The air that was supposed to reach $B$ doesn't get to there. Thus, the region $B$ has lesser air molecules than an unaffected control point $P$ or $C$. Since it is the number of molecules in a region that determine the pressure,
lesser the molecules per unit volume lower the pressure
Region $B$ has a lower pressure than $C$. Molecules move from $C$ to $B$ creating suction at $C$.