The flight instructor reported that, during a touch-and-go landing in crosswind conditions and with the student pilot on the controls, the airplane touched down on the runway centerline "but without perfect longitudinal (heading) alignment," and the airplane then veered left. The instructor took control of the airplane and added power to take off, but she did not retract any of the "partial" flaps. She maintained the "slightly" offset direction from the runway during the takeoff roll, and the airplane became airborne as it exited the left side of the runway. The left wing impacted trees and brush. Subsequently, the airplane came to rest at the bottom of a ravine. The airplane sustained substantial damage to the right wing. The instructor reported that there were no preaccident mechanical failures or malfunctions with the airplane that would have precluded normal operation. The airport's automated weather observation station reported that, about the time of the accident, the wind was from 330° at 7 knots, gusting to 14 knots. The pilot landed the airplane on runway 6.