Sounds to me like the magneto switch is "FLAT WORN OUT"... This subject is right up my alley, as I own and operate a aircraft maintenance business. First off, you should not be flying an airplane with a defective switch, (Instructors Fault) but mostly the maintenance departments fault. This should be caught during a 100 hr or Annual inspection. There are two airworthiness directives on ignition switches, depending on what brand of switch it is. There is either a Bendix switch or a ACS Gerdes switch which both have AD notes. By any chance is it possible to remove the key in any position other than OFF? I would not fly this airplane for safety reasons. As Flyfalcons noted, when you backfire and engine during a run up/ magneto check it possible to damage the exhaust system. As far as your instructor not doing magneto test,,,, find yourself a different instructor. Lastly, stopping the engine using the ignition switch is not the safest practice. There are some airplanes out there that this is the only to stop the engine, but now days the mixture is pulled to stop the engine thus starving the fuel system.
-Tom