Maybe all of these complex explanations could be simplified using a boat in water? Water moves. Boat on water moves in direction water is pushing. Controls on boat (engine and rudder) are used to move boat where the driver wants it to be. Engine and rudder must overcome/compensate for force of water trying to move it.

Rudder use in aircraft is no different.
Except when design of aircraft causes a ROLLING when using the rudder; that is the AIRPLANE's problem, not the physics of air mass on an object in it.