Character Analysis
First Day on the Job
Even though Hagrid's hut is in a different location—Cuarón had it moved to somewhere more scenic—his heart's in the same place. Hagrid cares for Harry and pals, and he cares for animals. He's a gentle giant with a heart of gold, even when it comes to magical creatures who could gut you with one claw.
That makes him a great new choice for Care of Magical Creatures teacher…but it also makes him a bit of a liability:
HAGRID: Look at him. Loves the smell of the trees when the wind blows through them.
That's Hagrid's opinion of Buckbeak—he sees the inner beauty of the animal, and ignores the sharp beak and talons. Hagrid has a blind spot for anything dangerous, maybe because he himself is so huge that it's hard to hurt him…physically, at least.
Emotionally, Hagrid is much more fragile. Insecure about his new teaching job, he turns to Harry for support.
HAGRID: How am I doing me first day?
Harry is, of course, there to support his friend. And he even saves Buckbeak. Sure, he probably wouldn't have if Sirius's life hadn't depended on it, but Hagrid doesn't have to know that. We won't tell him if you don't.