“I doubt it,” said Sirius. “I know [Umbridge] by reputation and I’m sure she’s no Death Eater —”
“She’s foul enough to be one,” said Harry darkly and Ron and Hermione nodded vigorously in agreement.
“Yes, but the world isn’t split into good people and Death Eaters,” said Sirius with a wry smile.
This quote presents an important theme in Order of the Phoenix, that the concept of "good and evil" is not a broad enough representation of the spectrum of morality; the world is a complex place filled with complex people. No one is wholly “good” just as no one is wholly “bad.” Everyone has the capacity to do good or bad deeds, or even morally grey ones. The introduction of this moral complexity goes hand in hand with Harry’s maturation and the beginning of the series’ true shift to a darker tone.
“I DON'T CARE!" Harry yelled at them, snatching up a lunascope and throwing it into the fireplace. "I'VE HAD ENOUGH, I'VE SEEN ENOUGH, I WANT OUT, I WANT IT TO END, I DON'T CARE ANYMORE!"
...
"You do care," said Dumbledore. He had not flinched or made a single move to stop Harry demolishing his office. His expression was calm, almost detached. "You care so much you feel as though you will bleed to death with the pain of it.”
Harry’s raw pain at Sirius’ death causes him to lash out at Dumbledore. Up until this moment, he had kept his feelings bottled up inside in an extremely unhealthy way, refusing to deal with his grief and the loss of someone he loved—not to mention the fact that he watched Sirius die, only causing further trauma. Rowling’s inclusion of this scene is her way of showing that it is okay to feel and grieve and care, and that you do not always have to be strong and stoic.
“He regarded him as a servant unworthy of much interest or notice. Indifference and neglect often do much more damage than outright dislike... The fountain we destroyed tonight told a lie. We wizards have mistreated and abused our fellows for too long, and we are now reaping our reward."
Dumbledore explains to Harry why Kreacher cannot be blamed entirely for his betrayal of Sirius. Dumbledore reflects with Harry on the injustices other magical creatures face at the hands of witches and wizards. The Fountain of Magical Brethren proposes a false narrative that wizards reign supreme over elves, goblins, and centaurs, and that these other magical races also accept human wizard supremacy. Dumbledore suggests to Harry that time is up, and wizards must answer for their centuries of subjugating other beings.
“Only Muggles talk of ‘mind reading.’ The mind is not a book, to be opened at will and examined at leisure. Thoughts are not etched on the inside of skulls, to be perused by any invader. The mind is a complex and many-layered thing, Potter... or at least, most minds are...”
Snape offers this tidbit of wisdom to Harry as they begin their Occlumency lessons together. Snape's statement pushes into the difference between Muggle's perception of magical processes and the "reality" of them; he also manages to sneak in an insult, suggesting that Harry's mind is, perhaps, not all that complex.
“Fools who wear their hearts proudly on their sleeves, who cannot control their emotions, who wallow in sad memories and allow themselves to be provoked this easily—weak people, in other words—they stand no chance against his powers! He will penetrate your mind with absurd ease, Potter!”
Another quote from Snape in Harry's first Occlumency lesson touches on the theme of love and preempts what Dumbledore says about how Voldemort is able to weaponize his enemies' capacities to love. Snape explains, or rather shouts, at Harry to impress upon him the fact that Voldemort will hone in on any emotional weakness or loving allegiance he detects in his enemies and use it against them.
“Dumbledore trusts him,” Hermione repeated. “And if we can’t trust Dumbledore, we can’t trust anyone.”
Here, Hermione argues for why they should trust Snape, despite his odious characteristics. Her statement reinforces the idea that Dumbledore is the be-all and end-all of wizards, the ultimate representation of what is "good" and "right," and further impresses upon the reader Dumbledore's sense of infallibility.
“Remember when that Sirius Black escaped, and there were dementors all over Hogsmeade looking for him? And now ten Death Eaters are on the loose and there aren’t dementors anywhere...”
Cho says this to Harry while they are on a date in Hogsmeade Village. Cho's observation draws both Harry and the reader's attention to the possibility that the Ministry may have completely lost control of the dementors.
“Sybill Trelawney may have Seen, I do not know,” continued Firenze, and Harry heard the swishing of his tail again as he walked up and down before them, “but she wastes her time, in the main, on the self-flattering nonsense humans call fortune-telling. I, however, am here to explain the wisdom of centaurs, which is impersonal and impartial. We watch the skies for the great tides of evil or change that are sometimes marked there. It may take ten years to be sure of what we are seeing.”
Firenze offers a more nuanced version of Divination that leaves far more open to interpretation. In past years, Divination is regarded by both students and teachers as a psuedoscience of the magical world which is reinforced by Trelawney's obvious fabrications. However, Firenze suggests that Divination cannot be understood by most beings and fully admits to the imprecision of the art of interpreting the universe.
“The thing about growing up with Fred and George,” said Ginny thoughtfully, “is that you sort of start thinking anything’s possible if you’ve got enough nerve.”
Ginny reinforces the theme of rebellion by citing her relationship with Fred and George as a source of faith in the possibility that with enough determination and desire, any rule or obstacle can be subverted.
"Youth cannot know how age thinks and feels. But old men are guilty if they forget what it was to be young... and I seem to have forgotten lately...”
Here, Dumbledore admits a year of shortcomings to Harry. He admits that he should have had more faith in Harry's ability to shoulder the reality of his situation, and even claims that Sirius' death is entirely his fault. If he had explained to Harry that Voldemort would use Legilimency to plant false visions in his head, he would never have thought that his presence in the Department of Mysteries was required. Dumbledore suggests to Harry that while age does bring wisdom, that wisdom is useless if it cannot respect the perspective of youth.
