Kakashi did not plan to kill his friend Rin actually, it was not his intention to execute him. Sure he was named Kakashi the friend killer but it was Rin who jumped into Kakashi’s chidori on the because she was the Jinchuriki of the three tails. There was a curse seal in Rins heart that would release Isobu onto Konoha and would cause destruction like the Nine tails however, Rin committed self-destruction by bouncing into Kakashis chidori so to spare Konoha the disaster.
Kakashi didn’t kill Rin, Rin commited suicide to herself, for the reason that she feared the three monster that were inside her, apprehensive that she may get controlled by this monster to annihilate Konoha, so she planned to break the seal in her using Kakashi’s Chidori, so while Kakashi was utilizing his Chidori on some fog ninjas, she bounced into this Chidori and passed on.
Rin, knew the Mist’s evil plan and then asked Kakashi to finish her. But Kakashi wouldn’t do it because he didn’t want to be known as a friend killer and furthermore not break the promise had promised his dear companion Obito Uchiha.
Thus, Rin chose to take it on herself-When Kakashi was going to strike a Mist shinobi, Rin hopped in the middle of and got herself executed by Chidori. Really, an extraordinary shinobi. She relinquished her life for her town.