Right, but if you just replace "pet" with "baby" in your comment, the argument is still relevant. I'm not saying either way is wrong, but I don't think you can immediately conclude that it's fair to bring a baby on a plane that disturbs the 30+ people in immediate proximity while obviously unfair to bring a small pet on board
It's not still relevant because a baby and a dog are not equivalent. A baby has rights a dog doesn't. A baby might disturb people, so might an adult, but both are humans and you have to take the risk of being disturbed by humans because society is made of humans. Society is not made of or for dogs. Dogs are optional.
The OP was not talking about small pets, which are already allowed. They're talking about buying a separate seat for a large dog. It is utterly insane to expect anyone to spend a cross-country flight with an 80lb Labrador next to them slobbering all over them.