Supposedly, cat food is bad for dogs. Is that really true, and if so, why?

This has been bugging me for a long time. Before you give me the common sense answer that dog food is for dogs and cat food is for cats, let me explain why I’m not satisfied with that answer.

Cats and dogs are both carnivores, though dogs are non-obligate and gain extra nutrients from non-meat sources. Right? Meat is the best main food source for both species. If cats are hard-core carnivores, then the nutritional value of cat food should resemble that of the meat, bones, etc. that they’d eat in the wild, right? A bird that a cat hunts wouldn’t be higher in fat or protein than a bird that a dog hunts. It makes sense to me that animals that dogs and cats both eat aren’t nutritionally better for dogs or cats. Chicken is chicken and rabbit is rabbit. So if cat food is made to nutritionally resemble prey animals (which I’m assuming), then why would cat food be bad for dogs? I could understand it being nutritionally incomplete (if dogs really need the non-meat “snacks” they eat) but actually bad for them?

The only answers I’m finding elsewhere are “because my vet said so” and “dogs and cats are different” sorts of answers that don’t really help me at all. And if you don’t have anything nice to say to me, please don’t say anything at all. I can’t believe how rude people were to me on a different site when I asked the same question.