I used to have a dog who was also terrified of balloons, and I've heard two theories on this.
One thory was that she was trained to stay off furniture by loading up the sofa with balloons that would pop when she got up, or the owner would pop one if she tried to get up. Either this theory is wrong, or that training method is ineffective, cause the dog loved sleeping on the sofa!
The other theory is that there's something really freaky to a dog about seeing a disembodies head floating around.
I also knew of a cat who developed a fear of pot holders. She got caught in the kitchen as she was trying to devour one of her owner's gerbils. Her owner reacted by grabbing a potholder from its magnetic hook on the refrigerator. In her haste, the hook and magnet went flying and clonked the cat in the head. From then on, she kept the cat away from her gerbils by hanging a potholder on the tank. And whenever a cake was ready to come out of the oven, the cat would bolt!