That's rubbish - I'll eat it if I'm wrong (2,3)
I believe the answer is:
my hat
'that's rubbish' is the definition.
(both are said to show you don't believe something)
I can't explain the remainder of the clue.
Can you help me to learn more?
(Other definitions for my hat that I've seen before include "Exclamation of surprise" , "Out of respect I might remove this" , "stuff!" , "Old-fashioned exclamation" , "nonsense" .)