"After being married for over 37 years, I showed extremely poor judgment by engaging in an extramarital affair. Such behavior is unacceptable, both as a husband and as the leader of an organization such as ours."
Imagine if this set an example for everyone, and every adulterer resigned from his/her job. Civilization would collapse, no? It would be worse than "going Galt" if everyone goes Petraeus.
It calls to mind the old "General betray us" ad, but he didn't betray us.
ADDED: Is the resignation really about the affair... or is it connected to Benghazi?