Having an affair opens yourself to blackmail, and given he is the top spy this is considered a serious offence. That's the thinking, anyway. There might also be an ethical code which was broken, which is a fireable offence.
The "susceptible to blackmail" argument is a justification and easy excuse. That is the exact same argument people used to keep gays out of the military for years.
Not to mention, it was leaked to the media, everyone already knows about it. How exactly could that be used to blackmail someone if the entire world already knows about it?
During the time when the affair was secret, Petraeus was vulnerable to blackmail. His failure to recognize that and alert his superiors demonstrates that can't be trusted.
Do you really think he would allow himself to be blackmailed rather than tell the blackmailer to go ahead and go public with the information? He admitted the affair to the FBI when initially questioned about the emails.
I suppose you think Clinton should have resigned (instead of lying about the affair, which made everything worse)?
What I think is irrelevant. The OP asked about the blackmail justification for resigning and my point was that in the context of the security regulations as they exist, having your affair exposed doesn't eliminate the need to resign. The rules as written require you to (1) not have affairs and (2) tell your superiors immediately if you break (1).
Now, maybe you think those rules are stupid. Frankly, I think some of them don't make a lot of sense (or at least fail a cost/benefit analysis), but I don't make the rules. Petreus agreed to follow those rules. If he didn't like them, he could have refused the job. Or he could have worked to change them. But he didn't. So he has to live by them. And he failed to do that.
I don't think we know enough about exactly what happened to determine if he broke the rules or not. People around him in Washington may have known about this for a long time before it went public.
For a lot of these military and intelligence positions, it is best to err in the direction of caution.
Also, the people involved have probably learned from painful experience that traditional institutional rules are usually better guides than they sometimes appear to be at the moment of decision.
I doubt that the top spy was fired for not sharing his secrets.
If anything I would guess that he was fired for allowing his secret to leak (which means incompetency).
Realistically though, all that scandal is just a cover for real reason why Petraeus was fired - probably something like policy disagreement with superiors.
