A well behaved dog would not just bite a cat, but that doesn't mean you need to pay all their vets bills.
This is my pet hate (pun intended).
The idea that dogs are mythical creatures without instincts of their own and that any dog that does not fit with a human-preferred behaviour must be a bad dog or must be badly behaved.
Dogs hunt. That is their instinct. Some dogs hunt more than others or perform PART of the hunt ritual more than others, because the instinct has been left intact or deliberately strengthened through years of breeding. Some dogs can be socialised with cats and learn not to chase them. Others cannot either through opportunity or because the instinct to chase them is too strong. Some can learn to leave alone a specific cat but will not apply that same rule to all cats (dogs are not great at taking a rule about one thing and applying it to anything similar, aka generalising).
We take terriers, breed them for generations to kill small, quick moving furry things then tell them they are bad dogs for biting a cat. We take sight hounds and breed them for generations to chase other animals then label them bad for chasing a cat. We take guardian breeds and breed them for generations to only every trust the speific animals they grew up with then call them a bad dog for chasing a strange cat.
No one labels a cat as a bad cat for killing a bird. No one labels a horse a bad horse for kicking out at the personw alking too close behind them. Or a fish as being a bad fish for jumping out of its tank when spooked.
The expectation put upon dogs to be something other than they are is unfair to them and denial on the part of the humans.