I'm torn on this issue because on one hand I have no idea why I should care or why it's on my news feed and on the other hand it's really fun to speculate.
Cheating is a funny thing. I've seen it justified in multiple ways and I understand the arguments and sentiment behind it but I still see no "valid" excuse for it. Going behind the back of somebody who trusts you not to is a horrible thing to do, especially when it risks STDs, pregnancy, or other repercussions (condoms are not 100% effective in preventing STDs). Open relationships are an entirely different scenario here because the couple has actually talked about it and they are okay with the decision.
At the same time, I don't believe this woman was a saint. She exhibits jealous and possessive behavior of a man that is already somebody else's wife. I think on some level she was stupid and young, but that argument only goes so far. I'm young and I'm not that naive. Getting involved with a married government official and hoping to gain anything other than liability is just plain moronic. In short, both of them made immoral and stupid decisions that greatly disrespected other people.
In this case he had a lot to lose from cheating and it seems like there's a risk of him having given away information to the woman he cheated with. You always get found out, even if the affair has been over for years, and when your spouse (or in this case the entire country you serve) finds out the wound will be fresh, new and brutal even though you've had time to get over it. I think there was not a lot of critical thinking going on here and that this guy has let his ego get to his head. He is no longer a good candidate for that high ranking position.
Personally, I don't trust anyone who shows that they make such poor life decisions to hold a high ranking defense position in government. This isn't even a moral thing, it's about common sense and having respect for other human beings.
I applaud him for stepping down gracefully though.