For years now I've speculated that Bungie became independent from Microsoft in 2007 because the studio wanted to make games that weren't Halo but Microsoft wanted no part of that. This conclusion seemed (to me, anyway) to be strongly supported by the spinoff deal that set Bungie free in exchange (at least in part) for Microsoft keeping the Halo franchise. Any lingering doubts I'd suggest were expunged by Jason Jones in his last interview with Game Informer:

GI: Before Destiny, your team had been working on Halo for a long time. What prompted the move?

JJ: You already answered your own question.

There you have it. Incidentally, the interview has some other good information about Destiny, the difference between story and world-building, and other stuff. I'm waiting to see if they ask him about whether Destiny will have a Body Count... I mean, Slayer mode.