I wouldn't go that far. I think the two artists had different approaches to making music and were at different stages in their lives in 1996.
Music-wise, Dre was and is a perfectionist, and would sit in the studio for hours upon hours working on a beat until it's right. In addition, he needed the strong motivation to work as well. In his early N.W.A days, it was to make it out of Compton, having the lavish lifestyle that they all dreamt about as kids. In his early Death Row days, it was to recover from leaving Ruthless and starting up a new company with Suge. In his early Aftermath days, it was to prove to everyone that he still had the magic touch and could make it on his own.
Pac, on the other hand, was a one-take kind of guy, and had new lyrics seemingly coming out almost as often as he breathed. In addition, he was always hungry, always out to prove something, and that seemed to always be more than enough motivation, hence his ability to record boatloads of songs. So obviously when the two of them are on the same team, there is potential for magic, but the two different approaches can cause problems.
Personality-wise, Dre was all into being a badass in the beginning, but toward the end of his stay at Death Row and after his own personal run-ins with the law, he was just tired of it, while Pac, fresh out of jail and a new Death Row artist, was out to prove he was the biggest badass in the industry, very much into the "chain is only as strong as its weakest link" meets "by any means necessary" type of mentality. So once again, conflict.
I don't think Dre hated Pac, he just thought Pac was probably always trying to prove something he didn't have to prove, which obviously turned out to be true. While Pac talking shit and calling Dre gay didn't help, I still don't see that as being enough to stir up hatred. I'd say he thought Pac was just immature when it came to the "riding." To put it into perspective, I just came back from McDonald's. I already graduated from college, and I saw some high school football players sitting in their little groups in the restaurant and trying to talk big and stir up commotion and attention. While I was once in their position, I look at them and realize that it's really just a waste of time, and hardly anything is getting accomplished, since there is so much more important stuff to put your energy into. I figure that's how Dre looked at Pac.