Flight Instructor reported the left main tire blew during a short field landing demonstration which resulted in the aircraft being disabled on the runway.

Narrative

The short-field landing [resulted in a blown tire]. The flight was conducted under 14 CFR part 91 as an instructional flight. The student previously had performed a short approach with a full stop landing. After; he demonstrated a short-field takeoff while remaining in the right close traffic. On the right downwind leg; I took over the flight controls intending to demonstrate a short field landing [technique]. I set the airplane to a gradual descent with flaps and speed changes to set the airplane on final approach with 30 degrees of flaps and 60KIAS. I had a 1NM stable approach to the runway while aiming for the threshold; so I could touch down on the Runway XX numbers. The touchdown was as intended; so dissipating the kinetic energy with the wheels on the runway followed. I promptly stepped on the brakes with aerodynamic braking while the wheels were on the ground. I try to use maximum braking; but the tires were slightly slipping while having directional control. I gather to keep the airplane on the center line while bleeding the energy but a couple of seconds before reaching a full stop the left hand tire suddenly deflated. At that point; I realized I had been too hard on the tires. After the left tire collapsed; I tried to exit the runway at the taxiway intersection; but the airplane was difficult to control with the flat tire; so I opted to wait for help in the airplane with the engine shutdown. The Tower Controller reached out to the Airport operations for assistance; and after 10 ~ 15 min I was towed out of the runway to our maintenance hangar. I checked the airplane and found the left-hand side tire damaged with a hole on the tread. I noticed in the preflight inspection both main tires were slightly bald with little tread; so I had in mind to be cautious about not using the brakes heavily; but it looks like I exceeded my force when breaking while demonstrating the maneuver. Overall; the mechanic replaced the left and right main tires. I need to be careful when braking not to slip with the tires; and not to perform short field landings when tires have little tread. I can substitute a real short field landing braking action for a 'simulating max braking' call out when dissipating the kinetic energy.