The plane can't go faster forward (relative to the belt) than the belt moves backwards (relative to the ground)

Did you notice how I never specified the exact wording of the riddle and you went off with your own interpretation and starting arguing about it? That's what makes it such an effective internet argument topic.

The riddle has at least two interpretations depending on the wording. Either the plane takes off with the wheels spinning at 2x takeoff speed (assuming they don't explode) or it's a paradox of logic.

Version 1: "An airplane taxies in one direction on a moving conveyor belt going the opposite direction. Can the plane take off?" = Yes.

Version 2: "The conveyor belt is designed to exactly match the speed of the wheels at any given time, moving in the opposite direction of rotation." = Logical paradox. To quite Cecil Adams:

This language leads to a paradox: If the plane moves forward at 5 MPH, then its wheels will do likewise, and the treadmill will go 5 MPH backward. But if the treadmill is going 5 MPH backward, then the wheels are really turning 10 MPH forward. But if the wheels are going 10 MPH forward . . . Soon the foolish have persuaded themselves that the treadmill must operate at infinite speed. Nonsense. The question thus stated asks the impossible -- simply put, that A = A + 5 -- and so cannot be framed in this way. Everything clear now? Maybe not. But believe this: The plane takes off.