You all fail to accept that there is relativity involved here. The speed of the treadmill relative to the plane is different to the speed of the treadmill relative to ground observer. I've said it before. In this example, the plane moves forward on the belt at a given speed. The belt moves backward at the same speed. By definition, the plane isn't going anyplace. If you apply more thrust, the plane moves forward faster than the belt is moving backward. In order to take off, the plane must move faster than the belt, otherwise its place in space doesn't change, only it's position on the belt.

Maybe this will clear things up for everyone. If you put a guy on the treadmill standing still and he shoots a radar gun at the airplane, he shows that it is departing his position at 300mph. The pilot shoots a radar gun down at the runway and shows the runway whizzing past at 300mph. Since by definition the treadmill belt is moving, the plane is stationary in space and thus has no air flowing over the wings and thus creating no lift. The engines are simply maintaining the aircraft's 300mph forward movement along the belt. If you shut off the engines, the airplane would drift backward until its wheels lost their inertia, then it too would begin to move backward at 300 mph.