I dont like to argue with my teammates, but if they are unnecessarily or unfairly flaming someone on the team, I will usually try and say something in that person's defense.
As an example, I had a match earlier tonight, where our top laner was being camped by the enemy jungler. He was trying his best, but by a few minutes in, he had died twice and they were pushing on the turret. Our jungler wasn't able to help because he was invaded level two and killed at the golems. And then when he respawned and tried to take the scuttle crab, the midlaner and jungler both collapsed onto him to kill him again. This happened so many times, that he was falling behind pretty far, and having to focus on trying to farm just to catch up in levels.
When the top turret fell, the top laner got pretty angry and started complaining about how the jungler had never ganked for him. But he'd been so busy with his own struggles, that he hadn't noticed how much trouble our jungler had been having. I noticed it, because as the support, I have to be watching the map for those sorts of things, and because a few of the times happened on bot side and when the jungler pinged for help, we had started trying to rotate.
It didn't seem right to me for the top laner to just start harassing the jungler, when he literally couldn't have done anything to help. He was too far behind after the two initial kills, which were before the 4 minute mark. So, I stepped in to say something. I just pointed out how far behind the jungler was because of the invades/camps, and that the jungler was even farther behind than the top laner! I don't think the top laner believed me, but he must have looked at the scoreboard, because he immediately stopped saying anything about the jungler. I also made a point of complimenting the top laner during the match, so that he wouldn't feel like he was just being disregarded or singled out. After all, it's a team game, and we needed all of us.
This sort of thing doesn't always work. If someone is too angry, or just too stubborn, it can be very difficult to diffuse them. But it never hurts to try a bit of diplomacy. As long as you are being polite, and not insulting or arguing with them, you're not violating the rules. And if it doesn't work, you can always just mute them.
