I doubt we'll ever hear the real reason he quit but my bet is that it became a "me or T.O.", and the front office chose T.O. because he fills more seats and sells more team schwag than Parcells does.
Parcells hated even saying the guy's name, but the front office has to maximize attendance and licensing revenue. Seems like it would be a pretty easy choice to make from an owner perspective...
Then again, I could be wrong. Still, I doubt we'll ever hear the real story.