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I came across the idiom, “get hold of the wrong end of the stick” in the following sentence of the scene where Barry Calvert, an FBI agent tells his colleague, Mark Andrews about the statement of an illegal Greek immigrant on suspected assassination scheme in Jeffery Archer’s fiction, “Shall we tell the President” P.37:

“I don’t believe a word of it,” Barry said immediately. “With his
English, he could easily have got hold of the wrong end of the stick. It was
probably quite innocent. People curse the President all the time. My
father does, but that doesn’t mean he would kill her.”

I checked the meaning of “get hold of the wrong end of the stick” with a couple of dictionaries:

Cambridge Dictionary defines it as “to not understand a situation correctly.”

The FreeDictionary defines it exactly in the same way as Cambridge - “(informal). to not understand a situation correctly”

Kenkyusha Publishing’s Readers English Japanese Dictionary defines it as “make an error of the judgment (of situation).

While the definitions of the above three English and English Japanese dictionaries are all “Situation specific,” Collins English Dictionary defines it as “a complete misunderstanding of a situation, explanation, etc.”

Can I use “get hold of the wrong end of the stick other than a “situation,” e.g. for meaning of word(s), message, statement, somebody’s notion, view, intent, and idea? Can I say “I get hold of the wrong end of the stick on his remarks (or instructions)”?

Secondarily, what is the origin of this idiom?

Correction:

I was reminded of that I dropped “end of the” from “get hold of the wrong end of the stick by TimLymington's advice.

It’s careless but a great mistake that occurred when I was transcribing the original text of Archer’s fiction. My apology.

I suspected if I should cancel this question. However, the definitions of all dictionaries of the idiom, and my question about whether the idiom is “situation specific,” or not remain the same.
So I ventured to leave it as it is by making necessary corrections.

Given that not a single reference work considers wrong stick as a variant of the well-known idiom, this corruption is likely to be a mistake (albeit quite possibly a deliberate one).

The origin of the two related idioms (see below) is thought be related to argumentum baculum or the argument of the cudgel (or staff, hence stick).
The best explanation can be found here.

The picture is literally that of a master beating a servant. If you get the wrong end of the stick, you are the recipient of the blows from the lucky master who holds the right end.

To say that you get the wrong end of the stick simply implies misunderstanding or wrong facts (and is not situation-specific, assuming I get the drift of your question).

To say that you have the short (or dirty) end of the stick is to have the least desirable part of a bargain or the worst end of a bargain.

Get hold of the wrong stick does not appear to make much sense. It implies there are a few sticks to choose from and (more implausibly) that one of them is right for the purpose. In the context provided, the author alludes to the subject's deficiency in the knowledge of English Language which could well lead to a misunderstanding on his part (a curse being misinterpreted as an actual plot to kill). It may even be the case that the distortion of this well-known idiom is deliberate and intended to disparage the Greek man's poor grasp of English.

The wrong end of the stick is at Question 67813 and linked to CUP Dictionary.

To get hold of the wrong stick is to misunderstand something completely: not even holding the right stick, let alone the right end of the stick.

The good news might be that even though you got hold of the wrong end of the stick, you didn't get hold of the wrong stick entirely.

The Student Room (UK)

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... once in a while, the foodie network in Atlanta really does get hold of the wrong stick.

Marie, Let's Eat (Woodstock GA)

I have never heard anyone using "get hold of the wrong stick", but "get hold of the wrong end of the stick" is familiar. Ngram seems to corroborate this experience.

I think it comes from Roman times. People who went to the toilet wriped their butt with a stick with something atratched to it, like a sponge or cloth. Obviously, if you were to get hold of the wrong end of the stick, your hands would get shitty