Flyjet,
When the FCOM says 1 and 2, I don't believe it means 1 then 2. For my money your instructor is being too pedantic if he is pushing this point. There are any number of arguments pro and con the order in which to shut the engines down (as my learned colleagues have already posted) but there is no technical reason for doing it in any particular sequence.
One further reason might be for standardisation if your airline flies 330s where (as I am told) there is a technical reason for shutting down engines in that order.
BN2A, You have never flown in China then.....definite death wish on the part of ground handlers over here!!