Some of it is by design, and some of it is either a game bug with the post BI patches or the "I'm the player. Kick me." sign. Prior to BI (or patch 1.3), you COULD ally with an ally of your enemy, and it would end the war instantly. However, whoever attacked would be kicked out of the alliance subsequently. Since then, using your situation as the example, Armenia wouldn't be able to ally with Scythia. However, that doesn't seem to work both ways. Scythia could offer the alliance to Armenia, which would end the war if accepted. The problem is the "broken alliance" isn't working like it used to, and I can't help but think it's broken. Now, instead of the party who attacks being kicked out of the alliance, it always seems to be the human player.

To use an example from my own experience, I was at war with the Seleucid empire. The Seleucids were allies with Scythia. My diplomat, talking with Scythia, didn't have the Alliance option even show up on the diplomacy screen. However, a few turns later, I was contacted by a Scythian diplomat who offered an alliance. I accepted and the war ended. When the Seleucids attacked again, I was out of the Seleucid-Scythia alliance.