Why did Obito spare Kakashi?
For Obito, Kakashi was a victim just as Rin was. He didn't blame Kakashi for killing Rin but rather for &quot;letting her die&quot; and not being able to keep his promise. He was aware of the fact Rin had the 3-Tails inside her and chose to die by Kakashi's hand.
Hence, he never resented Kakashi himself but rather the world that created this situation and forced Rin to commit suicide.
In chapter 600 of Naruto, Kakashi asks Obito if he blames him:

Kakashi: Aren't you going to blame me?
Obito: With this insignificant reality, what good will blaming you do?
Obito: I hold no interest in the affairs of this world that's about to disappear.