Yeah it’s not overanalysis, it’s bad analysis. There was one joke in one episode about Todd getting away with things because he’s white, it’s not some kind of thesis statement for his character. None of the rest of what he does makes sense as a commentary on white privilege. If his character were meant to be all about white privilege, which it isn’t, it would be saying that white people can get away with anything without ever experiencing any consequences, which would make it bad, ham-fisted commentary.
I know that people say you can’t analyze comedy, and that’s not true. However, you have to do so while acknowledging that it’s comedy. When Todd opens a dangerous unlicensed theme park that risks a bunch of people’s lives, it’s not the same as if a character in a non comedic show did the same thing, because the fact that it’s a joke changes the way it’s presented and the way it should be interpreted.
I don’t think it’s objectively wrong to read Dr. Champ as correct, but it feels kind of thematically hollow and not like something the writers would do, for a couple reasons:
Bojack’s issues mostly already have mundane, realistic explanations behind them, it just seems unnecessary and out of left field to add another explanation that doesn’t have much of a connection to the other, adequate reasons that have already been given. There is no horse who Bojack hates, where that hatred doesn’t already have a better explanation of some kind.
I don’t think it makes a compelling plot point. Bojack’s problems are all real things that exist, but the viewer has no context for what it means to “be a horse” and to feel guilt about that. As an emotional beat, it’s much easier to connect with his anger towards his parents as people as opposed to a hatred of horses. I mean, you could stretch it to be some sort of allegory for race/ethnicity, but six seasons in it just feels like a contrivance that wouldn’t add a whole lot to the story.
The viewpoint of the show is generally that self improvement is the result of work, not one-off epiphanies, especially ones that happen while drunk. It just seems a lot more likely that an “aha! this explains all my problems!” moment would be satirized rather than played straight.
Bojack idolized Secretariat all his life, that’s another counterexample besides Hollyhock. And, I don’t think Champ’s argument against Hollyhock as a counterexample actually makes sense. I think it’s true that Bojack sees Hollyhock as himself, but he clearly loves her. He hates himself for what he feels he’s become, not because he’s a horse, and he wants Hollyhock to go down a different path.
Bojack not knowing a lot of horses just kinda makes sense. There are all sorts of different animals in the world, not that many of them are horses, and Bojack doesn’t have that many close friends. It would also be strange to write additional characters in that are the same species as the main character without some reason behind it (e.g. his family members, Secretariat, and Champ). Like how two random characters in a show will almost never have the same first name unless there’s some reason for it, because even though that’s a thing that could just happen by coincidence in real life, it sticks out to the viewer of a TV show.
All that said, I do still think it’s open to interpretation, it’s totally possible there’s something I’m just not seeing here.