The Strange Case of Dr. Jekyll and Mr. Hyde is more than just a statement of the dementedness of 19th century scientists (recall Frankenstein). What Stevenson illustrates in this Victorian-era horror story is the innate desire of mankind to be guiltless monsters. While the rules of society constrain us, we secretly desire to do evil deeds.
Stevenson's story argues that the potential to ruin one's own social status is what keeps the monster in each one of us at bay. Reference to social image occurs throughout The Strange Case of Dr. Jekyll and Mr. Hyde, such as Enfield's encounter with Mr. Hyde:
"We told the man we could and would make such a scandal out of this, as should make his name stink from one end of London to the other. If he has any friends or any credit, we undertook that he should lose them."If status was the only thing keeping us from destroying each other, wouldn't we have completely annihilated our own species? If we were solely murderous, ravenous animals, our system of self-restratint would have broken down a long time ago. With one malicious mistake, the monster that has been trying to break out of its cage would escape and consume us. Perhaps then we'd forget all about social status, or merely find ways to conceal our crimes. Harmless members of society by day, but behind closed doors...

There must be something else that keeps us from being monsters.
Do we not all (or at least most of us) come equipped with some sense of moral consciousness? Stevenson's story neglects the human capacity for sympathy and its ability to create a naturally defined line between what is good and what is evil. Sympathy is the very foundation of many typical societal ideals, such as anti-violence. At times, sympathy causes us to feel compassion for complete strangers. Society is not built purely for the purpose of constraining us, but is rooted in one of the very things that makes us human. We are not all born innately monstrous - something evil in the world around us must ignite it.
References:
Stevenson, Robert Louis. The Strange Case of Dr. Jekyll and Mr. Hyde. Ed. Stanley Appelbaum. Roslyn, NY: Dover Publications, 1991.
GIF source: http://imgur.com/gallery/oVr9Y