The "Departures Control System" will not allow the same tag number to be printed twice (until the numbers have been round the clock!)
The only explanation I can think of is human error - the Emirates check in agent tagging someone else's bag with your tag, and your bag with someone else's tag. This does happen, but it's about a one in ten million chance! It is a breach of security, but wouldn't cause any concern as long as the other passenger actually travelled on the aircraft. (It could have had major implications if he/she hadn't travelled because the wrong bag would have been offloaded and, if he/she was a member of the pyjama clad gang, a primed and ticking item could have been left on board!)
Usually, the other person will realise they've got the wrong bag (or they have left it at the airport) and you will be reunited with it after a few days (once your description of the missing bag is matched with a baggage discrepancy). If not, you will then have be recompensed.