Q: Why isnt a fan pushing air in the direction of the fans blades? According to newtons law of reaction every force has a reaction in the opposite direction so why i dont feel any airflow near the sides of a fan, the fans blades are located in the sides of a fan, the fans blades are moving in a circular motion so the air should move in a circular motion too right? 

A: There are fans that push air or make the air move radially, these are centrifugal fans.
But the classic "propellor" type fan works the same as on an aircraft and causes an axial flow, the office fan blows towards you while the aircraft on blows to the rear so it moves forwards.
Given the picture, the air is pushed as the blade rotates due to the angle, or more correctly, the pitch of the blade.
