C172 Flight Instructor reported wheel brake failure during taxi resulting in a taxiway excursion and drifting into a ditch. Instructor evacuated plane and passengers and awaited airport personnel for assistance.

Narrative

Incident Report - Discovery Flight Taxi Incident On Day 0; at XA:00; I met with a father and his son (who joined in the back seat) for a Discovery Flight. These are flights where customers pre-purchase a voucher for a half-hour ground briefing and a half-hour instructional discovery flight. After spending about 30 minutes in the briefing room explaining the aircraft instruments; the rudder; and the basic structure of the aircraft; we proceeded together to the airplane. We completed a pre-flight inspection together; and I started the engine using the relevant checklist. After receiving a squawk from ZZZ Clearance; we were ready for taxi. During the initial brake check; the brakes felt softer than I typically experience; but the aircraft was able to stop normally at low RPM; and there was no immediate indication of a safety concern at that stage. I demonstrated the brake check to the student; and he confirmed a similar feel. I began a right turn to exit the parking spot and noticed that I needed to apply additional pressure (more than the usual) on the right rudder pedal to maintain directional control. We continued taxiing straight down the alleyway toward the left turn onto Taxiway 1. As I pressed on the left rudder pedal; I observed reduced responsiveness in the turn; and I attempted to assist with the left brake; but the turn remained shallow; and the right wheel moved slightly onto the grass. I reduced taxi speed and attempted to regain directional control by turning right toward Taxiway 2. At that point; I recognized that there was a significant directional control issue and decided not to continue with the planned flight. I was concerned about directional control during the takeoff roll; the ability to stop after landing; or the ability to exit the runway safely. I decided to return to parking to ground the aircraft and switch to another airplane. We continued straight on taxiway 2 with a plan to turn left onto taxiway 3; enter the runway momentarily; and then exit the runway at 4; to proceed back to the ramp; as the taxiway was too narrow for a safe turnaround considering the reduced effectiveness of the nosewheel steering and brakes. During the straight taxi; my seat moved back slightly into the next locking position; and I requested the cushion from the rear seat passenger to improve my reach and control on the pedals. This helped maintain better control while taxiing. As I reduced power to idle and pressed the left rudder pedal (also using some left toe brake) to turn onto 3; the aircraft did not turn at all. I visually confirmed that the student's foot was not obstructing the pedal and applied maximum braking; but the aircraft did not stop. I also attempted to engage the parking brake; which did not improve the situation. The aircraft continued moving slowly toward the ditch; and I shut down the engine quickly by turning the key to the OFF position to reduce any potential hazard. The aircraft rolled gently into the ditch and came to a stop when the right wing contacted the fence. Once the aircraft stopped; I immediately opened the doors; assisted the child out from the right side; and the father exited from the left side. I moved them away from the aircraft and confirmed that everyone was uninjured. I contacted the maintenance manager to report the situation and requested assistance. While waiting; I observed fuel dripping from the leading edge of the right wing and turned the fuel selector to OFF as a precaution. The maintenance team arrived shortly after and assisted in securing the area. The father and child were transported back to the terminal to meet their family. After ensuring the passengers were safe; I returned to the aircraft to retrieve personal items and to turn off the Master switch; which I remembered I had left in the ON position. When I arrived back at the aircraft; I was informed by the maintenance team that they tuned the master switch off. Later; the airport manager andanother person; arrived to document the scene; and the aircraft was later moved from the ditch; with permission; by maintenance. Maintenance started the engine and taxied the airplane back to the hangar under its own power.