After a moment of silence Ron says that Black and Lupin are crazy, and Harry points out that Black killed Peter Pettigrew twelve years ago. Black lunges for Scabbers, but Lupin holds him back and insists that Harry, Ron, and Hermione need to understand and have a right to know. Finally, Black stops struggling and agrees. Ron pulls himself up to leave but Lupin insists he stay and hold onto Peter. Black says that people didn't see what they thought they saw on the day that Peter "died."
Holding Black back and insisting that the trio needs to fully understand what's going on again shows that Lupin believes they're fully capable of handling this information like adults. He also recognizes that, if they don't get the full story, they'll never have a reason to question what they already believe.
In a trembling voice, Hermione says that Pettigrew can't be an Animagus because the Ministry keeps a register and would've known. Lupin laughs and tells Hermione that she's right, but there were once three unregistered Animagi at Hogwarts. He breaks off suddenly as the door opens. There's nobody there. Ron says that the shack is haunted, but Lupin says that the screams that used to come from it were his. He explains that he was bitten as a small boy and back then, the Wolfsbane Potion didn't exist. Dumbledore allowed Lupin to attend school and built the tunnel and the Shrieking Shack to keep people safe while he transformed. Dumbledore encouraged the rumors that the Shack was haunted.
Again, Hermione's insistence that there aren't unregistered Animagi shows that at this point, she still believes that the Ministry holds the absolute truth. As she learns that this isn't the case, she'll begin to come of age and learn to think more critically about things that are presented to her as fact. The same goes for the rumors surrounding the Shrieking Shack—in this case, while wrong, the rumors kept Lupin safe and kept people from investigating further.
Lupin says that his transformations were awful, but he had three friends—Sirius Black, Peter Pettigrew, and James Potter—all of whom eventually figured out where he went every month. Instead of deserting him, they spent three years figuring out how to become Animagi. They completed it in their fifth year and as animals, they could keep Lupin company since animals aren't in any danger around a werewolf. Because Sirius and James were such large animals, they could also keep Lupin in check and so they wandered the school grounds and around Hogsmeade. These explorations eventually culminated in the Marauder's Map.
What Sirius, Peter, and James did for Lupin was the ultimate act of friendship and sacrifice, as they made the worst times of his life into the best. This showed Lupin the power of friendship and impressed upon him that his friends would always be there for him. Though it's unclear exactly where Lupin has been for the last twelve years, his appearance also suggests that those years might have been easier with friends.
Hermione interjects that what they did was extremely dangerous. Lupin heavily says she's right; there were several times when he nearly bit someone. He feels extremely guilty now, as he's been inadvertently helping Sirius all along. He says that he never told Dumbledore that Sirius was an Animagus, as that would mean admitting that he betrayed Dumbledore's trust as a boy. This is why Snape has been so nasty to him. Black is surprised to learn that Snape is a teacher, and Lupin explains that once, Sirius told Snape how to get into the Whomping Willow. James learned what happened and saved Snape, but Snape did see Lupin as a werewolf. Harry asks if Snape is upset now because he thought Lupin was in on the joke, and Snape himself emerges from under the Invisibility Cloak and affirms this.
When Lupin is able to look back on the happiest time of his life and admit that it was also stupid and dangerous to have done that, it shows that while it doesn't compromise the great sacrifice that Lupin's friends made, it is possible to grow up and think critically about who he was as a young man. When the truth about the trick the group played on Snape comes out, it becomes clear that even though Black is beginning to shift to being a “good guy,” he does have a dangerous mean streak that affects whether or not people will trust him.