C172S Flight Instructor reported while aircraft was parked; student mistook BRS handle for parking break; resulted in BRS parachute system activated.

Narrative

I was giving the refresher flight to the pilot who wanted to practice some touch and goes from the right seat. The pilot has his Commercial Single Engine and Multi Engine Land License; Certified Flight Instructor license and about 250 hours of flight time on the same make and model of the plane (C172). After we completed the flight and performed all of the shutdown checklists we decided to push the plane to the parking spot which is located close to our hangar at ZZZ. It's worth to note that the parking spot is on a small uphill. I took the towbar and asked the student to push the plane by the wing strut. It turned out the towbar was broken (it was loose so I couldn't attach it to the nose gear). I decided to go to the rear of the plane and steer it by pushing the tail down and move it to the left/right. Once we moved the plane to the spot I looked around to find a chock to put it by the tire so the plane doesn't roll down but there were no chocks available in the vicinity of the plane. I still kept the tail preventing the plane from rolling down and asked the student to pull the parking brake so we could install the tiedowns. After the few seconds I hear huge 'BANG' and the shock wave threw me away from the plane. It turned out that the student activated the BRS parachute system in the plane. The airport fire/rescue team responded immediately and showed up on the scene about a few minutes later. It's also worth to say that the handle for the BRS system is guarded and in RED color. After I interviewed the student why he pulled that handle he responded that he didn't know what's that so he assumed that it has to be the parking break. Again; student had flown this make and model multiple times before.