The flight instructor, seated in the right seat, was providing tail-wheel flight instruction in an airplane equipped with wheel brakes only accessible to the pilot in the left seat. The flight instructor reported that he demonstrated the first landing to the pilot receiving instruction in the left seat. During the landing roll, he reported that he began to lose rudder effectiveness and the airplane started to veer to the right, so he applied full power to abort the landing. The flight instructor further reported that during the aborted landing, the pilot receiving instruction applied both toe brakes at the moment full power was applied. The flight instructor attempted to maintain directional control, but the left wing impacted the runway and the airplane veered off the runway to the left. The flight instructor reduced the power to idle and the airplane stopped in the terrain adjacent to the runway. The left wing and left aileron were substantially damaged. The pilot receiving instruction reported that he remained clear of the flight controls and brakes during the landing roll. He reported that he applied brakes only after the runway excursion to the left, after the flight instructor had reduced power to idle during the aborted landing. The flight instructor and pilot receiving instruction reported there were no mechanical malfunctions or failures with the airplane that would have precluded normal operation. Postaccident photos revealed deceleration skid marks leading off the runway first to the right, and additional deceleration skid marks about 550 feet further down the runway leading off to the left into the grass. The flight instructor reported the automated weather observing system about the time of the accident reported wind from 220 degrees true at 10 knots, which resulted in a 5 knot crosswind.