The original question was flawed in that it made the assumption that the treadmill could hold the plane and prevent forward motion.
Put a wheelbarrow on a treadmill and observe that no matter how fast you make the treadmill go, you can still move the wheelbarrow forward and back just fine => a plane can take off from a treadmill too
A planes ability to take off is based on AIRSPEED. Air flowing over the wing creates LIFT. The airspeed can be from the planes forward motion, of from a headwind, or both, but it needs airspeed. Period.
