The flight instructor reported that the purpose of the local flight was to perform an onboarding evaluation/training flight with a pilot that he had not previously flown the accident aircraft make and model. The flight departed and the pilot performed various uneventful flight maneuvers before returning to the departure airport. Both pilots reported that throughout the flight there had been a positive exchange of flight controls any time the controls were passed from one pilot to the other. Upon returning, the flight instructor demonstrated a stabilized approach and landing for the pilot receiving instruction. The pilot receiving instruction took the controls for a “normal” takeoff. The flight instructor reported that when the takeoff roll began, the airplane began to travel left of the runway centerline. The pilot receiving instruction then overcorrected resulting in the airplane being right of the runway centerline. He told the pilot receiving instruction to correct his heading, which resulted in another overcorrection. The airplane traveled left of centerline and continued toward the left side of the runway. The flight instructor attempted to add right rudder control input and reported that the airplane momentarily aligned with the “runway sideline” before the pilot receiving instruction added more left rudder and he was overpowered. The pilot receiving instruction reported that when the airplane began to veer off the runway centerline he corrected but “needed more pressure than expected” before the airplane veered left. The airplane departed the runway surface, and the flight instructor attempted to “hop” over the precision approach path indicator system, during which the right main landing gear impacted the system and was separated. The airplane touched down and veered right across the runway and an adjacent grassy area before coming to rest on a taxiway which resulted in substantial damage to the right horizontal stabilizer. The flight instructor reported that there were no preaccident mechanical malfunctions or failures with the airplane that would have precluded normal operation.