here's what i think
-the unlikely one: he killed Rin because Rin kept telling kakashi (like sakura to sasuke) how she loved him and whatnot and kakashi was going evil because he felt he let obito down. and like how sasuke was going to kill sakura, kakashi killed Rin.
-the most logical one: he killed Rin because rin probably knew about the MS and told kakashi to kill her so kakashi can get the MS so he can live and whatnot.
I really wish we get to know why he killed her XD i really want to know. maybe she was being controlled with a jutsu like ino's ?