There is a popular theory, sometimes called the Batman Villain fan theory or Bruce Wayne crazy theory, which suggests the caped hero is a patient at Arkham Asylum. The theory says that Bruce Wayne developed a life-altering mental illness after witnessing his parents' death, and had to enter Arkham Asylum since Alfred wasn't able to properly care for him. Instead of training to fight the bad guys who hurt his parents, young Wayne's psychosis became more severe, causing him to imagine becoming the hero Batman. While this isn't how comics typically play out, it does sound more plausible in the real world.
The theory further suggests that each of Bruce's imagined villains are a reflection of his own psyche, which he casts upon his fellow patients and health care workers in Arkham. Each villain represents a separate part of his mental state, as he uses his Batman fantasy as a form of personalized therapy. While some villains are insane, others are violent, and a few are sometimes caring. If you examine the main villains, this theory sounds more plausible.
Poison Ivy cares for and protects the ones she loves - even if they are plants. Because plants often can't care for themselves, Ivy's devotion to them is akin to Batman's compassion for the weak and innocent.
After all, it's easy to say plants are weak and innocent - that is, outside of the more animated ones Poison Ivy cultivates, of course. Batman's drive to keep Gotham denizens safe from the evils of his rogue's gallery mirrors Ivy's protectiveness over her plants. She will stop at nothing to keep them safe from harm, no matter if it's illegal or immoral. Batman breaks the law every time he takes on a bad guy to save the innocent, which is arguably exactly what Ivy does.
Leader of the League of Assassins, Ra's al Ghul is one of the deadliest and most powerful people in the DC Universe. While he may not have the ability to throw a mountain like Superman can, Ra's al Ghul has the power to sway governments and change history. One of Batman's most important philosophies is his code of justice and ethics, but Ra's al Ghul represents this code taken to the extreme.
Similarly to Two-Face, Ra's al Ghul's need to achieve order through chaos and directed action parallels Batman's moral code and desire for justice and order. The two achieve their goals in different ways. When you compare Ra's al Ghul's actions to Batman's, they are alike in style, even if Ra's al Ghul often takes a more intense path. This comparison helps to illustrate how Batman holds his code with importance, as not adhering to it is akin to following Ra's al Ghul's questionable ethics.
Batman is the night. There is a lot about his character that takes the element of fear and controls it. When you compare Batman to Scarecrow, the two characters employ the same tactics in divergent ways. Bruce dresses up as a bat because he always feared them - he is conquering his fears while using them to intimidate his enemies, a tactic also used by Scarecrow.
The difference revolves around their targets. Batman uses fear to prey on the strong, but Scarecrow uses it on the weak. Scarecrow's sadistic nature enables him to maintain control over others using fear, which is similar to Batman's use of fear, but for far more nefarious purposes. Ultimately, Batman wants to inspire fear in Gotham's criminals, while Scarecrow wants the entire population to fear him. Regardless of their motivations, it's clear Bruce sees the potential danger in his use of fear, by comparing his use to that of his shrouded enemy.
Selina Kyle's Catwoman is one of those characters in the DC Universe who has gone through numerous changes since her introduction. She has maneuvered from enemy to anti-hero and back again more times than anyone should, but ultimately, she represents a woman who does whatever she wants for selfish pleasure. Whether it's stealing something simply to obtain it or going against an enemy for personal reasons, Catwoman rarely follows the law.
Regarding Bruce, she represents his desire to skirt the law to achieve goals. Vigilantism is illegal, which means every time Batman throws on his cowl and punches a bad guy, he is breaking the law. Selina doesn't care about the law when it comes to achieving her goals. Batman also disregards the law, and while he may not go about killing people, he won't hesitate to put a criminal in the hospital.