SW seem to have made the right choice, which means the media will be all over them.
They either remove 2 people who pre-advised the airline of their dogs, one of whom relied on the dog for medical reasons (I'm assuming that's what the service animal is). The removed lady was not prepared to deal with her alleged allergy. She could have had a reaction in the air, causing the plane to divert at great cost to the airline and great inconvenience to the people on board. By removing that threat the airline did the right thing and ensured all the other passengers got on their way as intended. I am sure had the lady been more co-operative they would have moved her onto the next flight free of charge as a gesture of goodwill.