Why did Kakashi kill Rin?

Madara had white zetsu clone kakashi & rin so obito thinks it's really happening (while kakashi & rin could not even be there.. she could've died at a whole other time) or maybe just cloned kakashi, or somehow tricked the real kakashi & had him kill rin. it seems a little too coincidental that kakashi & rin would just happen to come near where obito was. obviously with them dead that would leave obito with no love, no friends & no reason to return to the leaf & also could lead him to want revenge etc basically it could benefit madara in a lot of ways. with no other info, there's no reason to think it's really kakashi that kille