Dogs bite children.
Minors and young adults need to be discouraged from interacting with dogs. Ways this might be accomplished is to restrict minors from owning dogs; putting warning signs at dog parks; prohibit humane societies from promoting the adoption of dogs; and prohibit broadcasting of Lassie, Benji and whatever those movies are with the Golden Retriever puppies.
The FBP&DC act gave the FDA authority to regulate dogs and anything it deems to be a dog.
("Deeming," by definition, is an opinion. It does not have to be supported by evidence.
Perhaps the FDA was also given authority over the dictionary.)
The FDA looked to the history of the AKC and concluded that any dog breeds developed before 1885 (when the AKC opened registration) would be grandfather in. Any breeders of dog breeds developed after 1885 would have to submit a pre-pet marketing application costing millions of dollars to prove, amongst other things: that their breeds won't encourage minors to pet them; won't incite people who don't like dogs to own them; won't cause people who used to own dogs, but don't want another one, to get one anyway; and that they are beneficial to public health.
Service dogs are exempt, since they are a medical
device.
And because they might encourage minors to pet dogs or people to substitute them for dogs, cats are deemed to be dogs.