The flight instructor reported that, during an introduction to soft-field takeoffs lesson, upon switching to the tower frequency, he and his student received the updated wind and altimeter setting. He noted that the wind was a "rear quartering crosswind" and that "I have done these before so thought I would be fine, though in retrospect [it's] been a long time since I have done [a takeoff] with similar conditions." During the takeoff, he held the yoke back with right aileron, and as the airplane began to lift off, he reduced back pressure on the yoke. After becoming airborne, the airplane drifted to the right and then settled back on the runway. He added more right aileron, rudder, and "back elevator," which reduced his forward visibility. The airplane became airborne again about 45 knots and drifted to the right of the runway centerline. He reduced power, landed, and came to a stop off the right side of the runway. The airplane was taxied back to parking with no further incident. A postaccident examination revealed that the airplane sustained substantial damage to the rear carry-through wing spar. The chief flight instructor reported that there were no preaccident mechanical failures or malfunctions with the airplane that would have precluded normal operation. The flight instructor reported that, about the time of the accident, the wind was from 300° at 10 knots. The airplane was departing from runway 7R.