Obito never wanted to destroy the world, he never did it solely for Rin. Think of it as a game of domino, one push and everything falls apart. Madara explained this, Obito's love for the world, all it took was one push to turn that warm love into deep hatred for the world. When Obito witnessed Rin's death, he lost everything, not just the person he loved. He believed in his friends, his sensei, the kindness of the world and its people. All that, everything he once believed in was lost with Rin's death.
Minato had promised he would protect the three of them, he failed to protect Obito, Rin and Kakashi. Kakashi promised he would do everything to protect Rin, yet he was the one to do the killing blow on her. Along with Madara's influence, Obito realized that the world was a type of "hell" and nothing ever went as people wished in this "hell". So he wanted to change the world, into a world where no one had to experience the same as he did.