Further to earlier answers;
The main thing preventing humans from flying is not the speed at which we can flap our arms, but the profile of the arm itself, and also the speed at which the air encounters the arm.
As a qualified pilot I have a basic understanding of the principles of flight. Human arms are not shaped for flying, like a birds wings or an airplanes wings, in as much as we do not have an aerofoil shape; we do not generate any lift no matter what speed we encounter air.
If our arms WERE shaped in such a way that they generated aerodynamic lift, this would not be achieved by a flapping motion, but by the speed of the airflow over the surface of the arm, similar to an aircraft taking off.
Birds do not generate lift simply by flapping their wings, but by other factors also, such as turning to face into the wind in the case of some larger birds or running/swimming up to the required speed to achieve take off as with some other birds (see particularly ducks taking off from the surface of a pond)
