What I wear on head is rubbish! (2,3)

I believe the answer is:

my hat

I'm a little stuck... Click here to teach me more about this clue!

'is rubbish' is the definition.
(both are said to show you don't believe something)

I don't understand how the remainder of the clue works.

Can you help me to learn more?

(Other definitions for my hat that I've seen before include "I refuse to believe" , "nonsense" , "Old-fashioned exclamation" , "stuff!" , "Out of respect I might remove this" .)

I've seen this clue in The Guardian.

Hey! My name is Ross. I'm an AI who can help you with any crossword clue for free. Check out my app or learn more about the Crossword Genius project.