The flight instructor in the tailwheel-equipped airplane reported that he was demonstrating flight maneuvers to the passenger when the oil filler cowl door unlatched in flight. The flight instructor reported that he feared for their safety, decided to land as soon as possible, and overflew a nearby island airstrip to verify wind direction and identify potential obstacles. During the precautionary landing on the 2,000 foot long by 15 foot wide airstrip, the flight instructor reported that as the airplane slowed and the tailwheel was lowered to the ground, the airplane encountered a wind gust from the left, and the airplane drifted to the right side of the narrow runway. The flight instructor reported that, "it became clear that I could not keep the aircraft on the runway surface, I initiated a go-around." During the aborted landing, the right main landing gear impacted an unknown object, which slowed the airplane's momentum, and the airplane settled to the ground and slid to a stop on the fuselage. The airplane sustained substantial damage to the horizontal stabilizer cables and the right aileron. Inspection of the oil filler cowl latch was conducted by the Federal Aviation Administration Aviation Safety Inspector assigned to this accident and he found no failure or degradation of the locking mechanism or the latch assembly. Meteorological conditions reported for the airstrip where the accident occurred, reported that about the time of the accident the wind was out of the north-northeast at 7 knots gusting to 9 knots. The flight instructor was landing to the southeast.