Could it be that Rin used some genjutsu on Kakashi and forced him to kill her.. This could explain why kakashi fell one floor, namely in the right moment when Rin died the genjutsu was released.
An explanation could be the following:
The zetsu clone told that Kakashi and Rin were surrounded by ninjas of the mist.
So I guess the situation was very desperate. An important thing is that this mist ninja did not talk about
her but
it.
I I suppose they wanted something in Rin's body. As at that time the second ninja war took place where the tailed beasts played a big role one possibility could be that Rin used to be a Jinjuriki. (This is just a theory)
Since a Jinjuriki dies when the tailed beast gets extracted I think if Rin really was one she would have dies anyway and decided to die without leaving the beast to the mist ninjas.
I hope we will find out soon.
What do you guys think about his theory?