A patient with cerebellar damage has full muscle strength and normal sensation in the arm, yet cannot bring a finger smoothly to their nose - the hand wavers, overshoots, and corrects. Why does losing the cerebellum produce this particular combination of intact parts and broken movement?

D. Because the cerebellum neither generates movement nor senses it.

The symptom tells you the function: strength intact means the motor path is intact, sensation intact means the sensory path is, and what has gone is the comparison between them. The finger hunts because the movement is launched roughly right and never trimmed in flight, a control loop running without its controller.