Naruto Thread (Spoilers For Sure)

I don't think Kakashi killed Rin to keep her from suffering, specially not when the enemy still wants her body even dead. Sure there are many things that could be happening but Zetsu said it has to do with experimenting bodies. My bet is they were testing some sort of drug on Rin capable of messing up with her mind and manipulate her or outright control her, Kakashi tried to save her but was found out, she woke up and attacked him and he had to kill her not to be killed. By killing her to save himself he totally breaks his promise to Obito and although Obito can't blame Kakashi, he can't forgive him either driving him mad and to the hands of Madara.

The role Zetsu/Madara play here probably is giving Rin away to the mist to trigger all the events.