Why would Paarthurnax help kill another dragon? Did I miss something?

At the very least, he'd help against Alduin. The only reason why Paarth is passive now is because Alduin acted up. He doesn't want other dragons to die though.. he wants them to learn the Way of the Voice. Although I'll doubt he'll get many followers.

I suppose if some of these dragons prefer Alduin's ways, then Paarth might help too. Not sure. That seems like a slippery slope for him. He might enjoy it.

well... ummm...

yeah.

1. he'd help if it benefited him to have that other dragon dead

2. he might help if he really believed in the way of the voice and that without that dragon other dragons might come over to his way of thinking

3. he might be willing to tell you how to do it because he doesn't care one way or the other what happens outside of the throat of the world

I choose to believe he believes in the way of the voice and that he's looking out for our best interests. I like dragons, and I'm a goof... lol

1. Paarthurnax helps because he managed to be the only dragon in history to have been able to empathize with man. As such, when he was called upon to help man learn the voice, he was more than willing. And this empathy managed to spread towards his feelings for his kin. It should be noted however that it isn't remotely easy for Paarthurnax to do what he's doing. Even after the thousands of years he's been the way he is he's still fighting his instincts for domination.

2. He doesn't follow the Way of the Voice. Paarthurnax came long before Jurgen Windcaller ever came up with that nonsense. Paathurnax only seems to be following the way because it falls in line with his own behavior. Its most likely that Windcaller based his philosophy on Paarthurnax's behavior.

Other dragons turned against Alduin, too.
- http://imperial-library.info/content/dragon-war
I'm pretty sure I ran across another reference somewhere that mentioned multiple dragons siding with mankind, too. Paarthurnax is just the one Kyne spoke to and instructed to teach thu'um.

How easy or hard it is is up for debate. Paarthurnax says that he constantly feels the drive to dominate again, but he doesn't mention it being particularly difficult to keep from going on a rampage. It's just instinct that he needs to keep suppressed. That he has you say hello by shouting fire in his face, though, shows that he's able to take it in stride, even after all these years of isolation (over a hundred since the last person reached The Throat of the World, and who knows how often before that).