Pet Parents
No.
You are not fluffies parent. You own an animal that perhaps views you as a pack leader at best, or food dispenser more likely. Its still a dog, cat, whatever, and no it can't come to the party leave the animal at home.
Having had just about every kind of pet there is and children, I'd say the experience has very little in common after they get out of the infant stage. If you think they are very similar you either treat your kids like crap, or spend way to much time and money on your dog.