Okay, one of my theories on why Kakashi killed Rin is that maybe Rin was a under cover spy sent from the Mist village. Why I think this? Well because notice how last manga The Mist ninjas says, "Shit he got us", "After we worked so much to get it". Hmm, what could they be talking about. Also in they say "At least retrieve the woman" "We mustn't let the enemy get the body". Why not? Isn't she supposably part of the Leaf?
Another Theory would be that put under genjutsu but that could be easily released. I was just thinking.:P and sorry about the images, I'm new to this!