The certified flight instructor (CFI) reported that the purpose of the flight was, in part, to provide the private pilot with recurrent training in furtherance of obtaining a flight review. The student was not current. Following performance of basic airwork in the conventional gear airplane, the CFI asked the student to perform a wheel landing. The CFI said that the student’s landing was successfully performed, but during rollout he exhibited a directional control deficiency. The airplane veered right during rollout on the subsequent landing, and the student attempted to regain directional control. The CFI reported that, due to his lengthy personal relationship with the student, he delayed acquiring control of the airplane. By the time he took the controls, it was too late to avoid the impending ground loop. As the airplane came to a stop on the runway’s gravel shoulder, the left main landing gear separated from the gear box, and the left wing broke.