Here are three idioms to talk about somebody being arrogant. Somebody who is arrogant; it means that they think they are better than everybody else. They think they are the best: they’re arrogant. It’s not polite, not a good way to be.
This first one is, we say: he has a big head. A big head; his head is big. Or maybe a “swelled” head, a swollen head.
To swell means make bigger. Swell, swelled, swollen. To be swollen. So, he has a swelled head. He has a big head. He’s very arrogant.
Another one is: to be stuck up. Stuck up. It’s a phrasal verb: stuck up. To be stuck up.
Like they have their nose in the air. “Oh, I’m better than everyone.” Stuck up.
It’s not polite to say somebody is stuck up. It means they are arrogant. They think they’re better than everybody.
And one more is to say somebody is full of himself or full of herself. “She’s so full of herself!” Full of himself. “He’s full of himself.”
It means he’s only thinking about himself. Inside, he’s just full of himself; there’s nothing else. He only thinks about himself. He thinks he’s number one. He’s arrogant.
Okay? Don’t be stuck up! Don’t be arrogant. Don’t be full of yourself or have a big head.
To have a big head, to be full of yourself, and to be stuck up. These are three ways to say that somebody is arrogant. Their nose is in the air.