I dunno...

Most of the people did a pretty good job explaing why exactly the plane WOULD move, and how it will be achieve. I guess it's hard for some to visualize. You're still imagining a scenario when the wheels would be delivering power to ground but they are not.

I like the "plane on ice" analogy. On perfect ice, the plane wheels would not spin, but simply slide along the ice with the plane moving forward once the engines are fired, resulting in the plane taking off.

In this scenario, ice is what eliminated the friction and allowed the place to move and take off.

With out original given scenario, it's the tires that are eliminating friction (perfect world with no rolling resistance, for the same of my point). Since there's no friction, it doesn't matter how fast the conveyor belt moves. It can move at 200 mph, BUT THE PLANE WOULD BE STILL WITH ENGINES OFF. I hope you're with me.

Now add the thrust of the engine. Bam! The plane takes off because the engine THRUST offsets the equilibrium of forces (again, keep in mind, we are not taking into consideration the rolling resistnace of tires and bearings).

If after 39 pages it's still not clear, I give up.