I agree with you. His execution of Rin was bad as well. He should have developed her more as a character and showcased her friendship with Obito to truly get where he's coming from. His execution with their whole situation was sub-par for me. To be honest, the only person who seems to be legitimately suffering from this is Kakashi. You also get what I'm saying when I mention that most of what Obito is doing is because of Rin, right?
In the words of Parrish: "Your haters be irate."
Yeah, Rin was the cause sort of but that's because something he believed was starting to see as truth but was skeptical, Madara had been telling/brainwashing for months that hatred is born to protect love, people have to die in order for others to live, but I guess you don't really take things like that on board until you are personally affected by it, Obito saw Rin as part of this cycle.
I agree though Kakashi must have suffered more, but Kakashi still had Minato and Gai, ever since Obito's 'death', he has only had Madara who had preached this philosphy to him and he had soon gotten to the point of no return. Don't get me wrong, he still isn't a great character and you're right, it still is about Rin but not in the way people make it out to be. The execution was terrible for their situation, no arguments there.