What semantic notions underlie 'chip on your shoulder' with the 19th US challenge to knock a chip of wood off someone's shoulder?

According to the Phrase Finder article on this expression,

"A 'chip on your shoulder' is a perceived grievance or sense of inferiority."

That definition of "a chip on [one's] shoulder" is not original to Phrase Finder, although the site doesn't specify the source. In any case, I think that the wording comes from Oxford Dictionary of Idioms.

This definition does not appear to be universally accepted as accurate, however. Before embracing it, let's see how it matches up with the definitions that appear in other dictionaries of idioms. I will quote from the ten dictionaries I consulted that have entries for the term, in ascending order, from earliest to most recent.

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Dictionary definitions and discussions of the idiom

From Longman Dictionary of English Idioms (1979):

chip on one's/the shoulder coll[oquial] a. feeling of anger or bitterness because one thinks that one is regarded by others as a person of little value or worth, e.g. because one lacks education or money: I'm sure he does give the impression of being rather a grouser...perhaps with a chip on his shoulder. I don't find anything of that at all. (The Listener 12 Sept 74) b. the cause of such a feeling: his own particular chip on the shoulder was his poor background {N usu. 2, after have, with, etc.} From a Former American custom. A boy wanting to fight would put a wooden chip (small piece of wood) on his shoulder. He would fight any other boy who dared to knock the piece of wood off

From The Wordsworth Dictionary of Idioms (1982/1993):

have a chip on one's shoulder to have rather an aggressive manner, as if always expecting to be insulted, ill-treated, etc: He is very difficult to deal with — he always had a chip on his shoulder about his lack of education. {19C[entury] US — a reference to a man who carries a piece of wood balanced on his shoulder in the hope that someone will give him an excuse for a fight by knocking it off}

From James Rogers, The Dictionary of Clichés (1985):

Chip on the Shoulder, Have a To be edgy, snappish, ready to fight. One would suppose a person with a chip on his shoulder would have all he could do to keep it from falling off. Apparently, however, it was once the fashion among boys for one boy to put a chip of something on his shoulder and dare another boy to knock it off. As a newspaper in New York explained it in 1830: "When two churlish boys were determined to fight, a chip would be placed on the shoulder of one, and the other demanded to knock it off—at his peril." This origin is also evident in the St. Louis Daily Pennant (1840) "Jonathan's blood is 'pretty considerable riz' anyhow, and it wouldn't take so much as knocking a chip off boy's shoulder to make it a darnational sight riz-er."

From Nigel Rees, Phrases & Sayings (1995):

chip on one's shoulder, to have a. Meaning 'to bear a grudge in a defensive manner', the expression originated in the US where it was known by the early nineteenth century. A boy or man would, or would seem, to carry a chip (of wood) on his shoulder, daring others to dislodge it, looking for a fight.

From Cambridge International Dictionary of Idioms (1998):

have a chip on your shoulder to blame other people for something bad which has happened to you and to continue to be angry about it so that it affects the way you behave | (often + about) Even though went to university, he's always had a chip on his shoulder about his poor upbringing.

From Merriam-Webster's Eleventh Collegiate Dictionary (2003):

chip on one's shoulder : a challenging or belligerent attitude

From Judith Siefring, Oxford Dictionary of Idioms, second edition (2004):

a chip on your shoulder a strong and usually long-standing inclination to feel resentful or aggrieved, often about a particular thing; a sense of inferiority characterized by a quickness to take offence. informal | In 1830 the Long Island [New York] Telegraph described the practice which gave rise to this expression: 'When two churlish boys were determined to fight, a chip would be placed on the shoulder of one, an d the other demanded to knock it off at his peril'.

From Martin Manser, The Wordsworth Dictionary of Idioms, revised edition (2006):

He's (she's. etc.) got a chip on his (her, etc.) shoulder He (she, etc.) bears a grudge or feels bitter or resentful about something: > 'He's got a chip on his shoulder because he can't read or write.'

From Robert Hendrickson, The Facts on File Encyclopedia of Word and Phrase Origins, fourth edition (2008):

chip on one's shoulder. In 1830 the Long Island Telegraph in Hempstead, New York reported that [same quotation as above]From this New York State boyhood custom, first recorded above, comes the expression to have a chip on one's shoulder, "to be sullen or angry, looking for a fight." The phrase itself isn't recorded until 1934, but is probably much older.

From Christine Ammer, The American Heritage Dictionary of Idioms, second edition (2013):

chip on one's shoulder A belligerent attitude or grievance, as in Mary is easily offended; she always has a chip on her shoulder. This term actually was defined ion a newspaper article (Long Island Telegraph, May 20, 1830): [same quotation as above] {Early 1800s}

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Analysis of the how and why the definitions vary

Six of the ten sources I consulted are British. The four U.S. sources are The Dictionary of Clichés, The Facts on File Encyclopedia of Word and Phrase Origins, The American Heritage Dictionary of Idioms, and Merriam-Webster's Eleventh Collegiate.

The four U.S. sources are striking in their focus on the element of belligerence in the expression: "edgy, snappish, ready to fight"; "a challenging or belligerent attitude"; "to be sullen or angry, looking for a fight"; and "a belligerent attitude or grievance." Even in the one case where the word grievance comes up, it is in the context of a belligerent grievance. That is, the U.S. authors are more concerned with the fact of the chip-bearer's aggressive behavior than with its possible origin in childhood deprivation, disadvantage, abuse, rejection, or whatever.

In contrast, the British sources seem far more interested in the psychological reasons underlying the belligerence. Thus, the "anger or bitterness" arise "because one thinks that one is regarded by others as a person of little worth or value"; the aggressive manner" comes "as if always expecting to be insulted, ill-treated, etc."; the chip-on-shoulder person "bear[s] a grudge," but does so "in a defensive manner"; the person "blame[s] others for something bad that has happened to [that person]"; and finally, the "usually long-standing inclination to feel resentful or aggrieved" shares space with "a sense of inferiority characterized by a quickness to take offence."

But even among the six British sources, the Oxford treatment of the idiom is an outlier. No other reference work in the group that I looked at takes the position that when we say that someone has a chip on his/her/their shoulder, we mean that the person feels inferior. In subscribing to that proposition, it seems to me, Oxford takes the idiom where most people who use it wouldn't be inclined to go.

The progression is straightforward enough: (1) The chip-on-shoulder individual is habitually or characteristically aggressive and belligerent—spoiling for a fight, as it were. (2) Such aggressiveness may well be explained as a defensive reaction brought on by a perpetual sense of resentment, grudge, or other grievance, typically related to past or continuing disadvantages that the individual has faced and may continue to face. (3) The underlying source of anger in connection with those disadvantages is a deep-seated sense of inferiority.

To my mind, this progression isn't semantical; it's logical (or psychological). And I'm not at all sure that it is justified by real-world usage. If it is justified (as the entry in Oxford Dictionary of Idioms suggests), perhaps adoption of the "inferiority" sense of the phrase is less pronounced in the United States than in the UK.

It may be noteworthy, as well, that the expression has been in circulation in the United States for a long time. Merriam-Webster's Seventh Collegiate (1963) has the same definition of "chip on one's shoulder" as the Eleventh Collegiate forty years later, except that it has "bellicose" in place of "belligerent": "a challenging or bellicose attitude." The shift from "bellicose" to "belligerent" happened in the Eighth Collegiate (1973). The full-size, multivolume OED of 1971, on the other hand, doesn't mention "chip on [one's] shoulder" at all in its extensive treatment of chip. The British take on the idiom may thus be accurate with respect to British sense and nuance, but not to U.S. sense and nuance. Or it may be an instance of relative unfamiliarity breeding misinterpretation.

Before closing, I want to address Robert Hendrickson's remark that "the phrase itself ("chip on [one's] shoulder") isn't recorded until 1934." This is a spectacularly incorrect assertion. Richard Thornton, An American Glossary (1962) lists multiple instances of figurative use of the idiom from the nineteenth century, starting with this one from the [Portland, Oregon] Weekly Oregonian (March 17, 1855):

Leland, in his last issue, struts out with a chip on his shoulder, and dares Bush to knock it off.

An Elephind search turns up many matches for "a chip on [one's] shoulder"—some literal and some figurative—from the middle of the nineteenth century onward.