[Spoiler] Kakashi killed Rin on purpose. Explanation.
I will make this concise:
Some people say that Kakashi accidentally killed Rin,
BUT if Kakashi accidentally killed Rin, he would have been shocked and his eyes would look like what it is shown on the right panel of this page:
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Notice his eyes. It is wide open because he was shocked upon hearing Obito's statement.
But take a look when Kakashi stabbed Rin with Chidori:
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His eyes are tearing. No one cries that fast upon shock. If Kakashi accidentally killed Rin, he'll first be shocked for a while, before tearing up.
Take a look again, his eyes are somber, as if he had no other choice but to kill Rin. If it was an accident, his eye would be wide open out of shock.
Now take a look again, his chidori is still active. If it was by accident, he would have withdrawn Chidori the instant he knew it was Rin. But as we have seen, Kakashi had time to cry, so he didn't withdraw Chidori on purpose.
EDIT: Another fact to prove my point, when Yahiko let Nagato stab him:
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Look at Nagato's eyes, wide open out of shock.
That's it, tell me what you think.