a few reasons why this might happen.
1. if you didn't buy that game off that gamertag it doesn't have the license so it can't play it offline. so say a parent account bought the game for you the all gt on that console can play while connected to live but only the one who bought it can while offline.
2.if you bought a new xbox and transferred hard drives you might need to transfer license.
i might be way off on this but lemme know if it helped.