Planes fly by virtue of Bernoulli's principle on their wings. Air being pushed under the wings only accounts for a small portion of the lift forces that make an airplane fly. The real lift forces results from the partial vaccum created above the wings (Bernoulli's principle). In effect, a plane rises on account that it wings are being "sucked up" from above.
To get the Bernoulli effect (and to lift the plane), the wings must expose a larger surface on top than below the wing. A curved wing does just that.
Second, we need to maintain a flow of air over and under the wings. This is the job of the engine, which pulls the plane and its wings forward, using a propeller. Once the airplane accelerates to take to a speed sufficient to generate enough lift for the airplane to fly, the airplane can take off. The way, a propeller is nothing more than a spinning wing - it also uses Bernoulli's principle to draw the airplane forward.