The problem I see here is that dogs are not just "animals". They're artificial creations of humans, and an invasive species when they're not kept as pets inside homes. There's a good reason that, for instance, in the Australian outback they kill, on sight, and feral cat they find: they're invasive species that predate the local native animal species to extinction. Animals do not have a right to live when they don't belong in a particular ecosystem, especially when those animals aren't even natural to begin with.

If we were talking about a native species of bear, things would be entirely different.