The flight instructor reported that while landing the airplane was slightly right of the runway centerline and he instructed his student to add left rudder, bring the nose up and hold it off the runway. The student added right rudder and the instructor believed also right brake. The airplane touched down on the left main tire first and when the right tire contacted the runway, the airplane veered to the right. The instructor stated that he considered a go-around but decided that it would not be safe and applied full braking. He did not attempt to steer the airplane back into runway alignment as he felt that doing so at the speed the airplane was at would also be unsafe. The airplane went into the grass alongside the runway, crossed a taxiway, impacted a taxiway sign, and then came to a stop. The student pilot being instructed had logged 8.3 hours of dual instruction when the accident occurred. The airplane incurred substantial damage to the left wing. The flight instructor indicated on his report that there were no mechanical problems with the airplane.