Yeah, but the dog is actually my essence, Yeah? There's a reason Padfoot is my Animagi form. And why I love being him so much, thanks, and don't disparage that please. Whereas I'd also argue that the wolf isn't necessarily the same for you. If you could do the Animagi thing, would your form be a wolf?
But yeah I see your point. Maybe it's the same point I'm making, actually, and we're just phrasing it differently.