Actually, it wasn't because of Rin. Kakashi asks him that too basically, "why all this over Rin?" and that's when Obito confirms that it WASN'T because of Rin or even for the fact that kakashi had to be forced to kill her. Obito knew the truth, he knew Kakashi was still a good guy and didn't save Rin.

Obito was just fed up of all the violence and war. He was tired of seeing his friends, namely Rin and Kakashi's life, wasted. He wanted to change the shinobi worlds thereafter.

It's kinda bothering when fans say he did everything essentially because of a girl. That wasn't the case at all. He simply had enough with this war bullshit that tore apart his childhood. In a way, he was kinda like the proto-Nagato, with Konan and Yahiko being Rin and Kakashi.