When you are running on a treadmill, the thing that propels you is your feet pushing backwards on the treadmill.
When a plane is taking off, the thing that propels it is the jet engines pushing backwards on air.
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When you are running on a treadmill you don’t move forward because the thing you are pushing on is moving the direction you are pushing, hence no force and thus you don’t move.
When a plane on a treadmill is taking off, the thing it is pushing on (the air) is stationary, hence force and thus the plane moves.