Similarly, different classes of vehicles get different licensing requirements; saying all cars are the same is just lazy, and a regulation meant for big risky entities being applied to small ones is what we call regulation moats. We have enough pet owners that we should be able to quantify risks and burdens for the purpose of licensing. Here we have an article which provides empiricism on the community burden from cats.
Cats are far more skittish around people as a rule. There are practically zero stray/outdoor cats that will attack a person unless they're backed into a corner and provoked. The same thing isn't true for dogs, some dogs are simply aggressive.
All good abilities when trained properly, if not, it's a recipe for a disaster.
It probably is related to the size of the animals. If there would be more tiger-sized cats and more Chihuahua sized-dogs it would most likely be different.
EDIT: Forgot to say, it don't matter even one bit what size the dog is or how small it is. If they aren't on your side, they're capable and very willing to bark at and attack you.