The key to the conundrum is that for the purpose of explaining the apparent forces on someone to whom a rotating frame of reference appears to define stationary, for example all human beings everywhere, centrifugal force may need to be taken into consideration since it appearappearss to be there although. Although it may be small depending on the speed of rotation. Which is what your girlfriend's textbook says. For the purpose of stating Newton's laws of motion in an inertial frame of reference, which is what your teachers were doing, there is no such thing as this centrifugal force. You might reasonably think that since they contradict, one of those points of view must be so stupid that nobody would ever say it. But that's not the case.
But the equations of motion in a rotating frame of reference are horrible, and the equations of motion in an inertial frame of reference are really simple. So, who cares about rotating frames of reference, to the point of giving a name to a "force" that doesn't exist in the inertial frames of reference that we prefer for calculation? People who live on a planet, is who. These non-existent forces have to be taken into account if you want to accurately compute the flight of a sufficiently long-range artillery shell or the movement of weather, relative to the ground instead of relative to some fixed point in space through which the earth rotates.
You are on to something when you speak about equal and opposite forces. Since the spinning object experiences a centripetal force, the object exerting that force necessarily must experience an equal and opposite force. The moon pulls the earth in its direction it, and the string of the poi pulls your hand in the direction of the poi. This is not what is usually called "centrifugal force", but it is away from the centre, and it "really" does exist.
