Attention: I'm not a teacher.
Your speculation regarding the idiom in question is right enough.
The phrase chip on one's shoulder means having a harbored grievance or sense of inferiority and being quick to take offence.
If someone has a chip on their shoulder, they are resentful about something and feel that they have been treated badly.
Carrying a chip on one's shoulder was a form of challenge in the same spirit as a medieval knight throwing down his gauntlet. If an opponent picked up the glove, or knocked the chip of wood off their shoulder, the challenge was accepted and the fight was on.