There is no simple answer to your question, though it is true that many people seem more tolerant of cat behaviour than of dogs. I have two dogs and one cat.
The fact is that the bites of both cats and dogs can be dangerous in different ways.
Most dogs have very powerful jaws, designed for ripping meat from bone and actually crunching and grinding bone itself. Therefore, they are capable of doing a lot of physical damage, particularly to soft tissue.
Cats may be less powerful with their bite generally, but they can still be nasty. In fact, they apparently often carry a far higher level dangerous bacteria in their mouths than dogs do, which can be injected under the skin of a human or other animal if they have chosen to bite. So although there us usually much less soft tissue damage from a cat bite, there is actually a greater risk of a serious infection setting in. There is some risk of that too from dog bites, but it is much greater from cats. I was told this by my vet when I had taken my poorly cat to see him a few years ago. I don't think it is widely perceived though.
Aggression in any animal may have many causes too, not all of them meaning that the animal is actually normally dangerous. These may include illness, injury, fear and annoyance (provocation from taunting perhaps). Dogs in particular can be very stoical when it comes to pain, and may show little sign of it until it is well advanced sometimes. They might then suddenly react to something in a way they never did before.
So, as I said, no simple answers. I would always advocate caution and respect and I am very big on insisting that none of my animals are ever unattended around young children, preferring to be safe rather than sorry. I do think though that zero tolerance is too simplistic.