Harry arrives in Dumbledore's office. It's near dawn and as Harry looks around, he thinks it's his fault that Sirius died. He feels stupid for believing his dream, especially when Phineas wakes up and snidely asks if Dumbledore needs him to send a message to Sirius. Harry says nothing and tries to leave the room, but it's locked. Phineas tells Harry that Dumbledore thinks highly of him, which only makes Harry feel worse. He feels trapped in his body. Dumbledore appears in the fireplace, greets the excited portraits, and tells Harry that his friends are all going to be okay.
Harry must now deal with the fallout of his trip to Ministry and face the reality of the first major loss he's experienced since he was a baby. Harry's sense of feeling trapped in his body can be read as the culmination of a year in which Harry has felt at odds with himself and unable to trust himself or what other people tell him about himself.
Dumbledore tells Harry that he knows how Harry is feeling, but Harry angrily insists this isn't true. When Dumbledore says that feeling this pain is Harry's greatest strength, Harry loses his temper. He shouts that he doesn't want to be human and feel pain, and he starts throwing things in the office. He tries to leave, but Dumbledore refuses to let Harry go until he has a chance to explain. He says that it's his fault Sirius died, though Harry shouldn't have believed his dreams. Dumbledore says that if he'd been open with Harry, Harry wouldn't have gone.
Harry’s anger has been stewing all year, and he really lets it out here. By taking responsibility for Sirius's death and suggesting that Sirius died because Dumbledore denied Harry information, Dumbledore makes it clear that knowledge is power—and that that power can keep people safe and shouldn't be underestimated. In apologizing for this, Dumbledore also apologizes for ignoring Harry for a year.
As Harry sits, Dumbledore confirms for Phineas that Sirius is dead. Dumbledore says that fifteen years ago, he figured that Harry would have a connection with Voldemort through his scar, and he suspected that Voldemort would find out about it. Dumbledore explains that he asked Snape to teach Harry Occlumency rather than teach Harry himself because he knew that Voldemort would try to spy on him if he knew how close Harry and Dumbledore were. Dumbledore says he saw Voldemort in Harry's eyes several times, and Harry remembers the feeling of wanting to bite Dumbledore. Continuing, Dumbledore says that Voldemort possessed Harry earlier in the hopes that Dumbledore would kill Harry.
While all of Dumbledore's reasoning is sound and makes sense, his mistake was in not telling Harry any of this reasoning. Given Harry's desire to leave Grimmauld Place when he feared Voldemort would try to hurt people there, it seems reasonable that Harry would've understood Dumbledore's fear that Voldemort would possess Harry and try to use him.
Dumbledore says that Sirius shared that Harry felt Voldemort in him the night he attacked Mr. Weasley, and this is why Dumbledore insisted Harry learn Occlumency. Dumbledore says that Harry dreamt of the door in the Department of Mysteries because Voldemort was obsessed with hearing the prophecy. Feeling guilty, Harry says he didn't practice Occlumency and that he tried to check if Sirius was home. Calmly, Dumbledore says that Kreacher lied to Harry. Over Christmas, Kreacher left the house, went to Narcissa Malfoy (who is related to the Blacks and therefore part of the family he serves), and has been passing information to her since, which allowed Voldemort to set the trap for Harry. When Snape alerted the Order about Harry's absence, Sirius insisted on going to the Ministry too and left Kreacher to speak to Dumbledore. Kreacher admitted to Dumbledore that he injured Buckbeak so that Sirius wasn't around when Harry called.
Now that Dumbledore is able to tell Harry about what his dreams of the Department of Mysteries mean, it makes far more sense why Dumbledore wanted Harry to learn Occlumency and stop the dreams. Again, Dumbledore's reasoning was sound and had Harry known any of it, he would've been far more motivated to practice and learn Occlumency—but instead, he had only his own curiosity and his hatred of Snape to guide him. The revelation that Kreacher lied shows that Harry was acting in good faith, but others around him weren't—and there was no real way for Harry to know that, given his limited information.
Harry feels his rage return and spits angrily that Hermione wanted them to be nice to Kreacher. Dumbledore says that Hermione had the right idea, but Sirius never took it seriously. He says that Kreacher is what he is because people made him that way, and Sirius never gave Kreacher a reason to behave loyally. Harry yells that Dumbledore shouldn't talk about Sirius that way and points out that Snape was nasty and dismissive when Harry tried to ask for help. Dumbledore notes that in front of Umbridge, Snape had no choice. Harry continues to blame Snape for goading Sirius and making Harry's dreams worse, and asks why it's okay for Snape to hate Sirius but not for Sirius to hate Kreacher. Dumbledore answers that Sirius neglected Kreacher; he didn't hate him, and neglect can do more damage than hate.
By speaking about Sirius in this way (that is, admitting his faults and naming them), Dumbledore encourages Harry to view Sirius as a multifaceted individual with faults, just as Harry had to learn to do after seeing James's bullying behavior in the Pensieve. Dumbledore's insistence that Kreacher has been neglected and is so irritable because of this neglect suggests that the first step to repairing relations with non-human beings is to regard them with respect and dignity. Sirius didn’t hate Kreacher because he didn’t consider him a full person—so Kreacher naturally sought out someone who seemed to value him instead.
Harry says that Sirius hated being locked up in the house, just like Harry hated being shut up and ignored at the Dursleys' house last summer. Dumbledore puts his face in his hands and asks Harry to let him share information he should've shared years ago. Dumbledore says that plenty of wizards would've raised Harry as a baby, but he knew that Voldemort underestimates the ancient magic of blood, love, and sacrifice. He says that because Lily died to save Harry, Harry is safe in her sister Petunia's house. Harry realizes that Dumbledore sent the Howler when Vernon tried to kick Harry out of the house.
Dumbledore's discussion of this ancient magic shows that within the Wizarding world, blood relationships are actually meaningful in their own way. Just as Sirius still inherited his mother's house despite being blown off the family tree, Harry is still protected by his aunt even though Petunia doesn't love him and never will. This conversation also clears up many mysteries going even back to the first scene of the first book, as Rowling continues to flesh out the series’ mythology.
Dumbledore says that after Harry fought Voldemort as a first year, he refused to answer when Harry asked why Voldemort tried to kill him. Dumbledore says that at this point, he should've known better. The years went by and Dumbledore continued to not tell Harry the truth. He says he cared for Harry too much and wanted to keep him happy, and was willing to do so at any cost. Dumbledore says that Harry has been ready for this information for a long time: Voldemort tried to kill him because of a prophecy, made before Harry's birth, that Voldemort heard only half of. Professor Trelawney made the prophecy to Dumbledore.
The introduction of a prophecy into the mix reminds the reader that in the Wizarding world, there's a fine balance between what's foretold and what people can control through their own choices. It was this information—the prophecy—that Voldemort was seeking and the Order was guarding throughout the book.
Dumbledore pulls out his Pensieve, puts a thought in the basin, and prods it. An image of Trelawney appears, and speaks the prophecy. She says that the person with the power to kill Voldemort will be born in July, and that Voldemort will "mark him as his equal." She says that one of them will have to kill the other: “neither can live while the other survives.” When it’s over, Dumbledore says that the prophecy could also have applied to Neville, but Voldemort chose Harry and "marked him as his equal" by trying to kill him. He explains that Voldemort's informant only heard the first half of the prophecy, so Voldemort never knew it'd be dangerous to attack Harry. Harry says he doesn't have powers, but Dumbledore says that Harry has the power to love. Dumbledore confirms that it's true that Harry has to kill Voldemort, or Voldemort will kill him, but declares that this isn’t because of the prophecy’s power—it’s just because Harry will have to do what is right. After a minute, Dumbledore says he didn't make Harry a prefect because Harry had "enough responsibility" elsewhere.
Though Harry has experienced a number of coming of age moments in this novel and in the last one, giving Harry this information is a major step. Now that he has this information, Harry knows what his future will hold and can plan accordingly. Note that though the prophecy makes several things clear, there's still a lot of wiggle room for Voldemort (and Harry) to make choices about how they interact with it and use this information. As Dumbledore tries to emphasize, even predictions aren't set in stone—and possibly, had Voldemort not known of the prophecy at all, he wouldn't have tried to kill Harry. Overall, this information makes Harry feel doomed but also like he has a degree of choice in how he will live his life.