The POH for the C 172N has the following direction. On the Prestart check list it says to place the fuel selector to "Both". On the Pre takeoff checklist it reminds you to double check the fuel selector is on "Both"
No where does the POH advise the left right both thing on the ground. This is another stupid flight schoolism mindlessly passed down from instructor to instructor.
I have never been able to find a record of an instance where a C 172 spontaneously stopped feeding fuel from one tank. The only instances were flights immediately after the fuel system had been disrupted by major maintenance, usually as a result of a wing removal. In these cases fuel lines blocked offs were not removed when the aircraft was reassembled. Obviously a very careful preflight and extra attention to all aircraft systems are required for the first flight after major aircraft maintenance.
So the result is the check the engine on each fuel tank "check" is designed to identify a problem that never occurs. Unfortunately what it does do is increase the probability that someone will take off after forgetting to reset the selector to both, something I have personally seen on several occasions.
Also if by some one in a million chance, there was a blockage at a tank it could take up to 10 minutes of running at idle power before all the fuel in the lines and carburetor was used up. So if you don't spend that long running on each tank you will have proved nothing.
Bottom line is the check is not required.
I also find it very discouraging that you have an instructor that could not explain why a check was being conducted. This is simply unacceptable. He/She should be able to explain exactly why every check is being preformed and what would be examples of an anomalous outcome.