I just had this wild theory after reading a recent thread. After Obito was crushed Kakashi may have tried to exact revenge on his killers and in the process become obsessed with it. Remember Kakashi always told Sasuke to never follow the path of revenge but generally only those who have followed the path of revenge and realised their mistake only advice in such a way. Now (here come the ball) what if Run was involved in killing Obito(would be perfect for a plot twist). Maybe she was not as innocent as she seemed. It is possible she was a spy. She knew Obito would come for her. Maybe she was working with Madara.What I mean is that she was evil or used in some way. When kakashi got to know this he had to kill her by orders from Anbu.
What do u think?