my guess, is that Obama’s people stated you go along with our side, in the upcoming investigation or we out you on this affair... and he probably said screw it, I won’t do it.. I’ll come out now with the affair, and resign..
More likely that Obama told him to buy into the cover story and Petraeus said "NO, I quit"...and the affair is simply a cover story.
The General would be advised to stay away from Ft Marcy Park.