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that the plane's speed is also relative to the ground because that is the assumed point of reference for everything.
That's pointless, because then, if the plane is going 25 mph forward, relative to the ground, then it is going 25 mph relative to the ground and it takes off. So why even pose the question of the myth.
Basically the myth should be cut off at "the plane is moving forward at takeoff speed, relative to the ground" and that would be end of story. You can say anything after that but it would not negate that you stated that the plane is going at takeoff speed relative to the ground.