Lift is not created by air being directed downward towards the ground.

An airfoil, or wing, has a greater surface area on the top side of the wing as opposed to the underside.

As air rushes over the airfoil, it must move faster over the wing, as it has more distance to cover, versus the underside of the wing.

This increased velocity of airflow over the top of the wing results in a decrease in pressure on the top of the wing.
This decreased pressure generates the lift.

Greater angles of attack can therefore create greater distance differences on the top versus bottom surfaces of a wing, resulting in greater lift.