It just takes one bad dog to spoil things for others. The dog in that story was growling and snapping. If she had lost control of the animal it could have bit someone. Then the airline would have been held responsible. Maybe the passengers could sign off that if an animal causes harm or mischief that the airline will not be held responsible but only the owner.
Maybe the animal owners should have to buy a special insurance policy for the duration of the flight.
And as has been pointed out some people have animal allergies.