When you use the expression ‘A Chip on Your Shoulder’ you mean someone has a
perceived grievance or believes others perceive them to be inferior.
Example of use: “You've got a chip on your shoulder if you think Dustin has something against you. He’s just a serious person; he never smiles at anyone.”
The origin of the phrase ‘a chip on your shoulder’ refers to a practice seen in America during the 19th century, in which boys spoiling for a fight would place an actual chip of wood on their shoulders before walking around belligerently daring others to knock the chip off.