It's often illuminating to actually read the classic books that have become famous cultural references...even clichés. Strange Case of Dr Jekyll and Mr. Hyde is an excellent example. Before, I would've parroted the common idea that Jekyll and Hyde are two sides of one person that are in constant conflict. Now, it's abundantly clear that the relationship between them is far more nuanced in the source. And this loss of understanding comes with a loss of the insights the book portrays about the tangled complexity that a person's private life can take on.
To start with, Jekyll admits upfront that he's always had a hidden side of himself, and it's a side that's had antisocial (...to say the least...) tendencies. His potion for manifesting the soul in a more direct bodily form merely provides a channel for that hidden side. The shallow interpretation that Jekyll is good and Hyde is bad fails immediately. Rather, Jekyll is the complex ambivalent whole and Hyde is one part temporarily separated. Hyde is Jekyll's opportunity to live out a private life freed from the blows to reputation that would normally be the consequences. He's Jekyll worst sets of impulses driving full-speed with all the brake lines cut. This is a form of freedom, despicable as it is.
The pair share memories and in that sense they cannot be separate people. Personal memory is part of the essential definition of what distinguishes one person from another. And, just like setting up the mundane details of a private life, Jekyll starts by being all too happy to accommodate for Hyde. Hyde is provided with his own entrance and own discreet servant. To his upstanding lawyer's alarm, Hyde has a right of inheritance to all of Jekyll's possessions if Jekyll is gone. Finally, there's the obvious point that Jekyll drinks the potion regularly to give Hyde time to enjoy himself. Two beings in all-out war wouldn't keep drinking the potion to let the other take over for a while. Jekyll wants to give himself over to his private life, personified by Hyde...at first. Similarly, Hyde is fine with escaping into Jekyll to preserve the neat arrangement. Private life or not, the pair need to continue to make a living and take part in the public life of society with its interactions with lawyers and bankers and so on. They each recognize the uses for the other. Hyde's psychopathic selfishness approves.
Yet again this is the source's greater nuance and allegorical insight. To me the text is explicit that Hyde isn't an unthinking beast, just as Jekyll is no perfect angel. In the time periods that someone is gratifying their immoral and/or socially-shamed private life, they remain capable of normal thought. As already mentioned, this capability to think about long-term ramifications is how they're able to justify giving up the private life's, er, liberties again. Hyde's lack of empathy or any concern for society, as well as the greater strength and speed of his passions, results in a truly despicable level of self-control in the moment. But he can form coherent plans, albeit fear-driven ones, and manage to speak with some minimal courtesy when he must.
Naturally, the conflict does develop further. The need for rising dramatic action demands it, of course. It wouldn't reach a climactic ending if it stayed in a harmonious compartmentalization of public and private lives. My guess is that more people manage this sort of split than we hear about—by definition these successes are quieter than the catastrophic failures. I'd say that the best moral is that people need to find a compromise between their desires and the rules they live by. Jekyll's hardly the first who's ever needed to find a productive or at least harmless outlet. Smacking strangers in the face is bad, but punching a punching bag isn't. An extremely strict society that has no place for meeting the needs of the whole person isn't great. Generally speaking people are better off when they live authentically instead of setting up a private life. I don't think that's much of a revelation these days, though.
The striking aspect of the developing conflict between Jekyll and Hyde is its similarity to the experience of the addict. As with an addiction, the actions of Hyde escalate. The urges that drive Jekyll and Hyde adapt by requiring more and more drastic acts to achieve the same satisfaction. With Hyde this is accelerated because he isn't repelled by the more drastic acts in the way that a whole person would be. Jekyll narrates that while releasing Hyde was difficult in the beginning, his growing adaptation to Hyde gives him greater hesitation—represented by requiring greater doses of potion—in going back to his complete self. At the same time, he feels obligated to spend more and more effort undoing or compensating for the shameful things he does as Hyde. He feels that he's begun to go too far, but like an addict he cannot give it up or slow it down. After all, Hyde's appeal to Jekyll is a lack of moderation: normal limits on the self are inactive in that persona.
As if all this weren't intriguing already, the story makes another fine point that rings true: the revenge of the private life is that the lines blur. His mounting horror and desperation about his private life is accompanied by increasingly spontaneous switches to Hyde. One subtle effect is that this can be simply embarrassing, given that Jekyll's clothes are too big for Hyde. Addicts too are subject to any embarrassments that their out-of-control addiction leads to. Furthermore, he's eventually unable to conceal Hyde from his staff at home, in the manner that addicts are rendered unable to conceal their addictions from close associates over time.
Jekyll becomes so fearful of transforming that he puts off sleeping or relaxing his self-resolve. The side of him that's primary is arguably changing from Jekyll to Hyde, bit by bit. Hyde was akin to a mask worn by Jekyll, but is Jekyll becoming more akin to a mask worn by Hyde? The more that a particular identity is engraved into someone's brain, deepening neuronal paths, then the harder it is to disrupt its activation. Reactions that are appropriate for the second identity start to cross over. Jekyll stops playing with fire by embracing Hyde, but he continues to feel the desire to give in, as if Hyde is growing restless. This is like someone who discovers that a starved urge will "take on a life of its own" after it's been indulged many times. When he releases Hyde to get some relief, Hyde's passions are stronger than ever.
Then Hyde does his worst, which as everyone knows is "hitting rock bottom". Hyde is in trouble with the law and escapes by switching to Jekyll, who's absolutely contrite now. After rock bottom, he's more than eager to cut off Hyde altogether. Only now is the shallow picture of "good and evil sides fight" relevant. Again like an addict who's recovering by remaking himself, Jekyll commits himself to doing all the good he can and resuming his normal life before the potions. And again again like an addict in recovery, he's protected from the temptation of Hyde by his feelings of repulsion at the kind of person he once was.
For him there cannot be a happy ending. One day he's feeling particularly complacent about his present moral superiority, and in that moment Hyde returns. His fear of the law's punishment motivates him to try to mix up the potion, but an ingredient is unavailable. He locks himself in at home, only for others to assume that he's murdered Jekyll and break in. He resorts to suicide; in fact Jekyll has been murdered at last by Hyde.
While an eternal battle of good and evil is a superb theme in its own right, I must say that the day by day struggle to keep caring is one that resonates with reality better. If one's EEEEEEEVIL side grows into a formidable enemy, that's usually because we've made it into one ourselves. In the past I might've agreed that there's a terrible Hyde evilness lurking in every "human heart from conception"; now I'd rather say that we as humans just have the starting material, both biological and cultural, that we've inherited over many many generations. It's up to us to choose what to do with it.