The only thing politics has to do with my response is that I know who Sarah Palin is, but my response would have been the same if you'd posted the photo from Ellen's show [or any of those photos]: parents should teach their offspring to respect the animals they encounter, period. And yes, it is about "what could happen", because that's the basis of most of what we teach small children. They don't understand the moral abstract, yet.
I mentioned subservient because that's the dog's place in the family 'pack', and everyone, including the dog, knows it. That doesn't make it ok to stand on them, or pull their tail & ears, or kick them. Teaching them that fact regarding a dominant family member generally isn't necessary, as they will pretty quickly be set straight if they try it with an older sibling. Exceptions occur, but that doesn't alter the need to teach them what they should know. Dad allowing a child to sit on his shoulders is Dad's choice, one hopes.
The cat can sit wherever it pleases - not a parent's job to teach them anything. And it would be a thankless job if they tried, I hear.