Protecting her by killing her? ...LOL that doesn't make any sense. He obviously did it for the village, that's why it was such a hard choice. Rin obviously had somekind of ability or knowledge of somekind, that could have terrible consequenses for the village, when falling into the wrong hands. So Kakashi was just doing his job, which is keeping the village as the priority number one.
i'm going to try and make sense of all the madness going on and throw some theories into the mix.
1. if they are surrounded by kiri-nin and anbu, and kiri is where akatsuki is rumoured to have started, and it concerns experimental bodies, then it could be sasori controlling kakshi through information delivered by hidden white zetsu clone. Think about it, one of the wars(i think the third, may be wrong) was caused by third kazekage disappearance which means by then, sasori was part of akatsuki which is rumoured to have started in kirigakure.
2. also, i entirely believe it was ochestrated by madara or he at least had a hand in it as he seemed pretty sure obito WOULD BE BACK!
3. also, i think word had spread that rin had successfully transfered a living organ and worse, a sharingan eye, with mere scrap tools, something no other medic-nin has done and it made her highly valueable(think back to kushina experience with kumo and remember kiri had ao who has byakugan). kakashi knew he was fodder and rin was target so he probably decided to kill her so they dont take her alive, syphoon her intel and medic skills and then take obito's eye or at least the eye of any uchiha unfortunate to die in battle. He probably did it knowing after she died, he can fight them suicidally and die then and there for not keeping his promise but was not counting on passing out, waking up alive and alone and living a long 30 something life of regret. Wooh, am winded.
