If you think about this as a weight & balance problem, you'll understand why the downward force of the airfoil is, indeed, weight.
no, if you think about it as a w&b problem you still get a force
vector that points downward, representing lift.
Your statement that the CG effects the weight of the airplane is a fallacy. If I move a 50 lb box from the front of the airplane to the back I havent changed the weight but I most certainly have changed the CG.
The CG defines where the axis of rotation for the airplane is going to exist. The reason this changes the flying characteristic of the airplane is because the lift is acting in somewhere on the wing, known as the Center of Lift. The distance between the center of lift and the center of gravity is a distance. when you take the force generated at the center of lift (which is a
vector) and take the cross product with the
vector representing the arm you get a torque (the direction of which is the axis of rotation).
This torque acting alone would cause the airplane to pitch. The magnitude of this force is directly proportional to the distance between the center of lift and center of gravity. Increase the distance, increase the torque.
The horizontal stabilizer counteracts this pitching moment by creating a torque of its own. In order for the torques to cancel, (assuming the CG is between the center of lift and the tail) the lift the horiz stab generates must be in the opposite direction. It is a simple force balance problem (physics 101).
"Weight" only acts through the center of gravity. If I'm flying with the nose below the horizon such that my thrust vector is below the horizontal plane, is my engine creating weight along with thrust? I think not. And before you try to argue that down arrows are only "weight" if they are below the axis of the airplane, consider that physics is the same whether or not i choose to use natural or cartesian coordinates.
Oh, and to the OP, ask your professor if the lift created by the tail contributes to drag during flight (which it does). When he affirms that there is drag created on the horizontal stab, ask him how "weight" is creating this drag, particularly one that can vary with airspeed. Perhaps that will get him to rethink his position.