OK… The question assumes that at the instant (which has the properties of a ‘point’ – position, but no dimension) the airplane starts moving forward the conveyor moves backward. Thus, the airplane doesn’t actually move forward from an external frame of reference (i.e., someone standing on the ground to the side). However the airplane isn’t touching the treadmill. It rests on its wheels. The wheels turn.
Imagine a tank. Its tracks are like big metal conveyor belts. Now put the tank on the conveyor belt. The driver tries to move forward. The conveyor belt moves backward at the same speed. Now get this: The track actually touching the treadmill does not move in relation to the treadmill. But the tank moves in relation to the tracks. Imagine that you put a tape mark on the track near the front of the hull. Put another piece of tape on the treadmill right abeam the tape on the track. Now do the experiment. To an observer sitting on the tank the tape on the track and the tape on the treadmill will appear to move backward. Until the tank’s track turns up when it reaches the rear of the tank, and the treadmill turns down as it goes around the rear roller, the tape on the track and the tape on the treadmill will mot move relative to one another.
Now let’s say this is a very wide treadmill and you are standing on the treadmill right next to the tape mark at the front of the tank. When the driver tries to move the tank forward you see that the tape on the track and the tape on the treadmill do not move in relation to where you’re standing. But the tank appears to move forward. To someone standing on the tank, he thinks he is standing still and it appears to him that you are moving backward. To an outside observer the tank appears to be standing still and you appear to be moving backward.
Consider a wheel is like the tank track, only instead of having a long flat bit it’s circular. The part of the wheel that is in contact with the treadmill moves with it just as the tank track does. If you were standing on the treadmill the airplane would appear to move forward.
So the airplane does move forward – in relation to the treadmill.