Cats and dogs, probably not (unless you count breeding of some pedigree species as dangerous to them).
However, we’re dangerous to many other species in the wild and our activities have caused many species to become extinct. We need to understand the effects we have on the environment and how complex it is. Each species depends on many others, sometimes. We can then do things to reduce the impact we have on the world, and to help endangered species to recover. This is already being done in some parts of the world.
I think that humans can be dangerous to any and every species on the Earth if we want to be. I don’t think there is any animal on the planet that we can’t kill. What stops us being dangerous to these species if that we don’t want to harm them.
I have to agree with Will. We are generally very protective over cats and dogs in this country. You can’t really use them in testing and there are strict laws on the way you can treat them. I think at least here they aren’t at a huge danger from us.
In terms of them harming us, it is more likely that people will become allergic to them, than them being dangerous.
I think that cats and dogs are safe. I think that the human mind generally gets too emotionally attached to animals, simply because they are so cute. Even if we imagine the food that we eatas a fluffy little bunny, or a cute litte chirpy chick, it puts a lot of us off eating, so I think that animals are generally fine.
What I do worry about is humans being dangerous to other humans. We’re a complex, confusing breed, us humans!