You have some quasi-military ideas going on here. The instructor is usually more experienced, but senior is the wrong word.
"The student must follow the Instructors direction?" No. When they are in the aircraft, the instructor as PIC has the authority that they have over any other passenger, to ensure the safety of the aircraft. Other than that there is no "must" about following directions.
"Can not legally fly without the Instructors approval"
The instructor needs to authorize the flight. That is different to command, e.g. the instructor cannot command the student to take off.
Line authority? No such thing in a civilian flying school. More complex in the military, where a student might be higher rank than the instructor so the student does have line authority, and line authority and PIC must obviously be 2 different things.
You are pulling in every possible meaning of command, rather than what it means in this specific context.