Character Analysis
This is the film where things start to get really interesting for Snape's character. Particularly at the end.
But we're getting ahead of ourselves...let's back up.
Double-Agent Wizard
Snape is now officially playing for two teams: Team Death Eater and Team Dumbledore.
Both teams know that he's playing both sides—but it's all good, because each team thinks Snape is only pretending to be loyal to the other. Only Snape knows for sure where his true loyalties are. And we have to admit: we sure can't figure it out.
We should note that Snape hasn't necessarily convinced everyone on each side. As you know, Harry has disliked Snape since they met and definitely doesn't trust him, and he has skeptics on the Dark side as well.
For example, Bellatrix Lestrange (a lifelong member of Team Death Eater) doesn't bother to hide her doubts when she accompanies her sister, Narcissa, to ask Snape for a favor early on in the movie. Narcissa is Draco Malfoy's mother, and apparently the Dark Lord has given him some kind of special mission that makes Mama extremely nervous. Narcissa begs Snape to help her son, and he agrees.
Bellatrix decides that's not enough, though, and makes Snape seal the promise with something called the "Unbreakable Vow," which means there will be seriously nasty consequences if he breaks his promise. Also, she makes him promise that he will complete Draco's mission if the kid fails. Yeah, this doesn't bode well.
So, even if Snape is loyal to Dumbledore's crowd, we know from the start of the film that he's made an unbreakable promise to do something pretty nasty for Team Death Eater. So, he's probably not going to be endearing himself to Harry and/or his friends (and/or us) any time soon.
Oh, and to add to our suspicions that Snape may not be fully on Dumbledore's side, we hear a kind of nasty confrontation between the two of them towards the end of the film. In it, Snape seems to be balking at Dumbledore's orders:
SNAPE: Have you ever considered that you ask too much, that you take too much for granted? Has it ever crossed your brilliant mind that I don't want to do this anymore?
DUMBLEDORE: Whether it has or hasn't is irrelevant. I will not negotiate with you, Severus. You agreed. Nothing more to discuss.
Hmm, not sure what that's about. You'd think that if Snape was really trying to be disloyal, he'd be hiding that fact and not arguing…hard to say. We're so confused.
Half-Blood Prince
So, we should also mention that Harry finds this textbook from someone calling himself the "Half-Blood Prince," and following this guy's margin notes turns Harry from a crummy Potions student into a total star. Even though it seems like a bad idea to be taking advice on spells and potions from some unknown dude, Harry is all about the Prince and his marginalia.
Well, until he uses a spell from the Prince's book to disable Malfoy in a fight, and it turns out to be really nasty.
Harry gets rid of the textbook right after that, but he ends up using the spell on Snape in anger at the end of the movie (we'll get to that in a minute) and discovers…yes…you guessed it: the Prince of Potions was Snape himself:
SNAPE: You dare use my own spells against me, Potter? Yes, I'm the Half-Blood Prince.
We should have known: a former student with a knack for potions and a dash of sadism? That sounds like the Snape we've come to know for sure.
Dumbledore's Man…Or Dumbledore's Murderer?
So, yes, back to why Harry really wanted to hurt Snape...well, there's no easy way to say it: Snape Avada Kedavras Dumbledore at the end of the film.
Kills him.
Hits him with the Killing Curse and knocks him out the window of a high tower.
It was not an accident, and Dumbledore even begs him not to:
DUMBLEDORE: Severus. Please.
At least, that's what we think has happened, no?
In any case, Snape has finished Draco's mission (which we now know was to kill Dumbledore) and kept his promise.
We're not sure if this is all part of some master plan to prove his loyalty to the Death Eaters and continue to play double agent, or something else entirely. But if it is, Snape appears to be the only person who knows for sure. The only living person, that is.