Malfoy remains in the hospital wing until Thursday morning, when he comes to Potions halfway through class. Snape idly tells Malfoy to settle down and Harry scowls; he knows that Malfoy is playing up his injury and that Snape would've yelled at him if he'd come in late. Malfoy sets up his cauldron next to Harry and Ron and asks Snape for help cutting his ingredients, since his arm is in a sling. Snape makes Harry and Ron help Malfoy, which gives Malfoy the opportunity to smirk, feel superior, and tell them that his father is going to get Hagrid fired.
Harry's side note about the way that Snape would treat him indicates that Snape doesn't treat his students impartially. This begins to set Snape up as a bad teacher and an unethical one at that, as playing favorites means that Malfoy may not be held to a high enough standard while Harry will have to work twice as hard to learn anything.
At the next table, Neville struggles with his Shrinking Solution and his fear of Snape makes the subject even harder for him. His potion is supposed to be green, but Snape berates him when he notices that Neville's potion is orange. Snape tells Neville that they'll test his potion on his toad Trevor at the end of class and instructs Hermione to not help Neville.
Berating students also shows that Snape is an awful teacher, while suggesting they test the potion on Trevor shows that Snape is cruel and doesn't care about Neville or his pets. By forbidding Hermione from helping, he also tries to ensure that Neville will fail.
Seamus asks Harry if he's heard—there's been a sighting of Sirius Black nearby. Malfoy gives Harry a mean look, asks Harry if he's planning on catching Black, and says that if he were in Harry's place, he'd be seeking revenge. Before Harry can make Malfoy explain what he means, Snape tells the class to clean up so they can test Neville's potion. Harry notices Hermione whispering instructions to Neville.
It's telling that Harry thinks twice when Malfoy indicates that there's something more to the Sirius Black story than Harry knows already. It suggests that Harry isn't willing to question adults—he trusts them—but because he doesn't trust Malfoy, everything he says is worth scrutinizing.
Snape calls the class to gather around Neville's cauldron. He gives Trevor a few drops of the potion and Trevor turns into a tadpole. Sourly, Snape administers the antidote and takes five points from Gryffindor since Hermione helped. Ron grouses about Snape as they walk to lunch but stops when he realizes that Hermione is no longer behind them. They see her hurrying towards them, and she insists she had to go back for something as her bag splits. Ron looks at the book she hands him and asks why she has it—it's not for a subject she has today.
Again, Snape clearly prioritizes making Neville feel horrible. He abuses his power instead of actually teaching his students anything about potions—or for that matter, praising the students that do understand the material and are capable of helping others. With this, Snape turns his classroom into a place that isn't safe and where nobody can learn.
Later, the Gryffindors sit in the Defense Against the Dark Arts classroom with quills and parchment ready. Lupin arrives, announces a practical lesson, and leads the class towards the staffroom. They run into Peeves the Poltergeist on the way, and Lupin shows the class a spell that sends the gum Peeves was stuffing in a keyhole into Peeves's nose. They find Snape in the staffroom. As Snape starts to leave, he warns Lupin to not trust Neville with difficult tasks unless he has Hermione to help him. Mildly, Lupin says he'd actually like Neville to help him with their first exercise. Neville turns red as Snape leaves.
Nobody likes Peeves, so this spell is a surefire way for Lupin to start building rapport with his students and show them that he's on their side. Lupin continues this endeavor when he so calmly defends Neville to Professor Snape. This suggests that Lupin knows how Snape likely treats students in his classroom, and that he sees it as his responsibility to undo some of the damage that Snape is doing.
Lupin leads the class to a wardrobe and explains that there's a boggart inside. Hermione defines a boggart as a shape-shifter that takes the shape of whatever scares a person most, and Harry says that the class has an advantage because there's so many of them, the boggart might not know what shape to take. Lupin leads the class through a defensive charm, "riddikulus," and then asks Neville to join him. Neville nervously tells Lupin that he fears Snape more than anything, and then with prompting, tells Lupin about the clothes his grandmother wears. Lupin instructs Neville to think of his grandmother's clothes while he says the charm, and Snape the boggart will be forced into Neville's grandmother's clothes.
The fact that Neville's greatest fear is Professor Snape reinforces just how poor a teacher Snape is, since Neville doesn't fear him just because he's not good at Potions. It's possible that Neville could be passably good at Potions if Snape didn't terrorize him so much, which suggests that it's Snape's fault alone that Neville is so bad at his class. This exercise with the boggart allows Neville to face his fears in a safe, supportive environment, thereby encouraging him to trust Lupin.
Lupin asks the rest of the class to think of what scares them the most and how to make it funny, as they'll take on the boggart in turn. Harry first thinks of Voldemort but realizes he fears the dementors more. Lupin begins the exercise before Harry is ready. Neville successfully forces the boggart Snape into a ridiculous dress and hat. Several other classmates tackle the boggart but before Harry has a chance, Lupin steps in. The boggart turns into a white orb, and Lupin asks Neville to finish the boggart. After Snape once again ends up in Neville's grandmother's clothes, the boggart explodes. Lupin gives out points and assigns homework. Harry leaves the class feeling sad. He wonders why Lupin didn't let him tackle the boggart and wonders what Lupin thinks of him.
When Neville so perfectly fights the boggart a second time, it shows what a little bit of confidence from a good teacher can do: this is a full turnaround from Neville's performance in Potions, with a teacher who thinks little of him. Harry's fear that Lupin thinks poorly of him or doesn't think he's capable suggests that Harry understands that at Hogwarts, he can't trust that teachers will actually treat him fairly—Snape is proof of that.