Responses
You have to think with the mentality of a time when animals where considered inferior to humans. Dogs were used to hunt and to guard houses. Dogs also are impulsive and have instincts, so saying that you're a dog implies lack of intelligence. It's basically comparing a human being to a beast which cannot comprehend human interaction and acts only with the aim to fulfill its primordial instincts
Why is being called a "dog" an insult? Dogs are great. Don't insult dogs by comparing them to the emperor's shitty behavior in the past. Surely there's gotta be something more appropriately terrible to call the emperor, no?