C172 flight instructor with student reported a loss of control during taxi when the right brake malfunctioned. Instructor regained control and aircraft was towed to ramp.

Narrative

This event occurred on Day 0 while going out on a Part 61 training flight.The flight was conducted in a C172S model.Prior to starting our taxi; we performed the appropriate brake checks in the ramp area with no noted defects. After requesting clearance for taxi ZZZ Ground assigned us 'Runway XX taxi via 1 and 2'. We initiated taxi; with the student at the controls. Initially we taxed without any problems; following appropriate taxi procedures and speeds; but after establishing on taxiway '2' the student made a statement saying that the rudder controls started to feel weird; and the student responded by pulling the throttle back to idle; with my consent. Our Ground Speed indicated roughly 10 knots at the time of throttle idling; and subsequently started reducing. Immediately there after the airplane started pulling to the left; and the student quickly informed me that he was losing control of the airplane. I then quickly took the controls of the airplane and rapidly applied full right rudder; while applying full right brake. The rudders and brakes felt mushy; and yielded no response resulting in the airplanes continued pull to the left. The airplane moved at a slow rate of speed while slowly drifting off the taxi way centerline. Eventually the airplane came to a stop slightly off the taxi way; at which time I proceeded to contact ground control to inform of the situation. My immediate assumption was that the rudder cable might have snapped; and that was the initial information I incorrectly relayed to the ground controller. After the airplane had come to a complete stop; I proceeded to pump on the brake pedal; and after a few pumps I felt the pedal starting to resist and the right brake came back to life. This allowed me to realign the nose towards the taxi way centerline; but with safety in mind the decision was made to get the airplane towed back to the ramp; rather than attempting a taxi back. In conclusion we inadvertently lost control of the airplane due to a temporary loss of right brake effectiveness. No property; person or airplane was damaged during this event.