Ok, I've determined something about the AI. Specifically, part of how it gets mad about people going to war.
If AI 1 goes to war against you, and you defend yourself, the other AIs keep track of how that will affect everybody. Will that hurt trade with people they also like, and make money off? Would it benefit them if they helped you? Would it benefit them if they fucked you up the ass? Will they be seen as warlike by other Civs if they help you destroy another nation?
They recognize things that you are superior in. If you have a strong economy, they would love to trade with you to benefit from that. If you have a strong military, they may want to be your friend just in case shit happens, or alternatively, they may see you as a threat and conspire against you.
The reason everyone might declare war at the same time on is because on their own, they each see you as the biggest threat. In that they all see you as the biggest threat to victory, they will ask others to form their own pacts of secrecy against you. This isn't Civ 4 with +2 to relations from years of peace bullshit. This is stopping your opponent before they can achieve victory, especially before you become too big a threat.
You were attacked by one civ, so you wipe them out? Making the war too costly for the attacking civ is often more than enough to stop the war. Wiping out their civ wasn't needed. Just take a little, not everything.
That is the difference between being seen as a peacekeeper or a dictator, the allies or the axis. If you wipe out that other Civ, they will be especially mad because you just said "if they look to take the Rhineland, then not only will we fight back, we will have Germany cease to exist."
You just eliminated the old Nazis, and now, YOU are the Nazis. Time to stop the Nazis again!
Just because someone has a pact of secrecy and/or cooperation with you, doesn't mean you are their lifetime ally. If you get a pact of secrecy against Civ 2 with Civ 1, that doesnt mean KAY GUYS let's go annihilate them! It means "we will work together as they are currently a threat to myself. Don't go overboard."
If you think it means that, then they weigh the benefits of eliminating one threat that was larger versus preserving the goodwill of everyone else by washing their hands of what you just did. By yourself making you a larger threat, they by proxy would be a threat as well.
It's not that they don't want that guy gone. It's that they don't want a huge target on their back.
Everything about Civ 5 Diplomacy I learned from the Israel threads in the OT. True Story.