Here's my theory why Kakashi killed Rin:
First take a look at this page from chapter 604:
Here we see Kakashi killing Rin who is SURPRISED from that !
Many of Naruto Fans said 3 different reasons why Rin was killed by Kakashi:
1. She was a spy
2. Rin wasn't really her,it was White Zetsu
3. Obito was on Genjutsu
I was so confused why Kakashi killed Rin but from what I see at last chapter,I think I know the real reason
Take a look at one page of last chapter now :
Here we see that Kakashi called himself TRASH because he didn't keep a promise and everyone learn that killing Rin was his decision!
Now,here's my theory:
Kakashi and Rin were covered by many Anbus of Mist Village who can learn a lot of informations from Rin and Kakashi like Ibiki and Inoichi do with enemys.Knowing that, Kakashi have to make a choice:
1. Giving up and finish in enemy's hands,from that Konoha would be in danger!
2. Saving Rin by killing himself but Rin would captured easy by Anbus of Mist!
3. Run off from them but because Rin would be slowest they would captured easy by enemyes!and 4. Killing Rin so him would run off faster and Konoha would be undamaged!
He was so sad to decide a choice like that but he have to kill Rin so A VILLAGE would be undamaged!
Even when he killed Rin,he didn't have much chakra to run off so he fell on the ground!
That's was my theory,but everything I hope will be shared in next chapter
What do u think?