To look at this from the perspective of animal owners: animals are not "pets" to them, they're family. To deny them bringing a dog in an airplane is like denying them bringing a baby in a airplane.
That argument cannot be randomly disregarded because it is a valid one. Dogs bark, babies cry. Dogs are unhygenic, and babies are little balls of filth.
Why should a dog fly in cargo because you don't like a dog inside the airplane? I don't like babies, does that mean we should put babies in a crate in the cargo section?