The flight instructor reported that the student pilot approached the runway with too shallow of an angle. The student applied forward pressure on the yoke, and the airplane's nose pitched down. The instructor recalled that the student's pitch application was excessive, and he called for a transfer of the flight controls. However, the student remained on the controls, and the instructor had to overpower the student's control inputs while the airplane was in a 45° nose-down attitude. The airplane landed hard in a level attitude, and the nose landing gear collapsed. A fire erupted in the cabin, and the instructor used the fire extinguisher to attempt to extinguish the fire. Subsequently, the airplane slid to a stop on the runway, and both occupants exited; the fire consumed the cabin. The airplane sustained substantial damage to the cabin and wings. The instructor reported that there were no mechanical malfunctions or failures with the airplane that would have precluded normal operation.