
Revealing mistake: When the weasels are at Eddie's apartment and Roger is handcuffed to Eddie, Roger runs under the bed and drags Eddie on the floor. As he pulls him you can clearly see a board with wheels under Eddie that is pulling him under the bed. (00:38:50)
Answer: There's really a lot of possible reasons he hates other toons. There's a whole Roger Rabbit book and comic book series that explain Doom's background more. In the film, he's greedy and wants to destroy Toon Town to build the freeway to make more money. In human disguise he's also seen as merciless and is just punishing toons to maintain law and order, etc. Although that's just an excuse to kill toons as well. However, not explained in the film; as a toon he was cast as the antagonist in cartoon films until an accident one day left him thinking he was an actual villain (as opposed to just an actor playing one). That's when he began his life of crime, including killing Teddy Valiant. So his hatred of toons is more about him being evil and not a personal vendetta against them, like Blade's motives.