The planes propulsion being air I can understand, but think of it this way.
If you have a plane, on a treadmill, the treadmill is stationary and the planes engines are at ‘tickover’
( please excuse the terminology)
If you then start the treadmill, surely the plane would move backwards?
You could then counter act that by throttling up the planes engines and bring the plane back to a stationary state.
Wouldnt it then be the case that as you increased the speed of the treadmill, you increased the power of the engines?
Then the plane still appears to be stationary?
I once met a man with a jet powered bicycle ( I kid you not, it was at the world wheelie championships at elvington). Shame we couldn’t get him and his bike on a treadmill and see what happened.