There is more to this story.
All the way back to petraeus rising in the ranks. Nothing to do with affairs. Everything to do with running weapons. Broadwell, it seems, was looking for signs or proof of corruption.
I would agree. His emails may have prompted an FBI investigation but I doubt that's what led to his decision.....
I suspect that Petraeus was being pressured by the whore to divulge classified information and realizing that he was now a national security risk and subject to blackmail, he abruptly resigned.