A change in speed would imply a change in kinetic energy. But, as we see from the diagram, there is no energy input to the system; for example no-one is pulling the thread through a distance. So there is no change in the disc's kinetic energy or speed. It follows that the direction of the string's pull on the disc is at right angles to the disc's velocity.

A change in speed would imply a change in kinetic energy. But, as we see from the diagram, there is no energy input to the system; for example no-one is pulling the thread through a distance. Neither is any work done against friction. So there is no change in the disc's kinetic energy or speed. It follows that the direction of the string's pull on the disc is at right angles to the disc's velocity.