It wasn't the specific death of this person, it was the meaning of the death. Rin was an innocent girl, a child, sacrificed for a war she didn't know the beginning or end of, in a plot to kill even more people. It was the realization that innocent children like Rin die awfully, for no reason, and that despite how badly he wanted to be a hero, he couldn't save everyone, that was what made him snap. It was the realization that his ideals of kindness and heroism weren't what the world ran on that made him give up. Above all, he himself was a child, a child that grew up without parents, that grew up in a war without parents. As I said with the Zuko example, or even the example about adults, that kind of stuff at such a young age could seriously mess a person up, now give them the idea that they have the power to stop all these awful things they've experienced from happening to other people, and that in doing so they could erase their pain and everyone else's, in Obito's mind state at the time, that he joined Madara, isn't too surprising.
