I focus on the 2nd theory, out of 2, for the etymology of 'chip of your shoulder'. How does limiting "the amount of timber that could be taken", thus the "revoking of their previous benefit", semantically shift to signify "perceived grievance or sense of inferiority"? They appear unrelated to me, probably for I don't understand the history of 18th century working practices at the British Royal Dockyards.
What's the meaning of the phrase 'Chip on your shoulder'?
A 'chip on your shoulder' is a perceived grievance or sense of inferiority.
What's the origin of the phrase 'Chip on your shoulder'?
Anyone who might be inclined to doubt that origin might be interested in an alternative theory. This relates to working practices in the British Royal Dockyards in the 18th century. In Day and Lunn's The History of Work and Labour Relations in the Royal Dockyards, 1999, the authors report that the standing orders of the [Royal] Navy Board for August 1739 included this ruling:
"Shipwrights to be allowed to bring [chips] on their shoulders near to the dock gates, there to be inspected by officers".
The permission to remove surplus timber for firewood or building material was a substantial perk of the job for the dock workers. A subsequent standing order, in May 1753, ruled that only chips that could be carried under one arm were allowed to be removed. This limited the amount of timber that could be taken and the shipwrights were not best pleased about the revoking of their previous benefit. Three years later, for this and other reasons, they went on strike.
Hattendorf, Knight et al., in British Naval Documents, 1204 - 1960, record a letter which was sent by Chatham Dockyard officers to the Navy Board, relating to the 1756 dockyard workers' strike at Chatham. The letter records a comment made by a shipwright who was stopped at the yard's gates:
"Are not the chips mine? I will not lower them."
It goes on to report that "Immediately the main body pushed on with their chips on their shoulders."
That's a nice story and does connect an incident concerning chips and shoulders with a belligerent attitude. We need to be a little wary of swallowing that derivation whole however. The problem with it is that the phrase isn't known to be recorded in print in England with its figurative meaning anywhere near the 18th century. The first such record by an English author doesn't seem to be until the 1930s in fact, in Somerset Maugham's Gentleman in the Parlour:
"He was a man with a chip on his shoulder. Everyone seemed in a conspiracy to slight or injure him."
A gap of nearly 200 years between the use of a phrase and the incident that supposedly spawned it in the same country is hard to explain. In my humble opinion, the 'chips on shoulders' report dating from 1756 refer literally to just that, chips carried on shoulders. There's no evidence at all to suggest 'a chip on one's shoulder' existed as a figurative phrase until the 19th century.