In episode 345 of Naruto Shippuden (オレは地獄に居る/I'm in hell), when Obito arrives on the battle field, he sees how Kakashi killed Rin. The wiki summarizes this scene as
On his way to the battle site, Obito has a vision of Rin through his empty eye-socket. He arrives just in time to see Kakashi run his Chidori through Rin's chest. Rin's death awakens both their Mangekyō Sharingan.
In the next scene we see that the Kiri-nin are clearly disappointed by the fact that Kakashi killed Rin, one of them says "Damn it! He did it!", and another replies "After all the trouble we went through to get her!"
But I don't understand why he had to kill her, why they couldn't wait, e.g., for reinforcements to arrive. Is there some good reason why it was better, for her, or for the village, that she dies, rather than to be captured by the Kiri-nin?