I always see the expression “his breath hitched” or “his breathing hitched.” However, as far as I can tell in the dictionary, the word “hitched” does not denote anything I can relate to breathing. Of course I understand what people are trying to get at when they say that expression, but is it technically correct? Does it make sense, semantically?
Learn English – Usage of “hitch”
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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.
Poetry writes its own rules. But if I saw "wax'd" in the same line with "withal," I would not be inclined to interpret "withal" in the one non-archaic sense that survives today (which Merriam-Webster's gives as "together with this: besides"). Rather I would suppose that it was being used in one of two archaic senses—either to mean "therewith" or to mean "nevertheless."
Other readers might associate it with the Shakespearean meaning "with," as in Rosalind's line in As You Like It:
I’ll tell you who time ambles withal, who time trots withal, who time gallops withal, and who he stands still withal.
Merriam-Webster's specifically observes that "withal" in this sense must be "used postpositively with a relative or interrogative pronoun as object"—which is why when Orlando asks "I prithee, who doth he trot withal?" Rosalind answers "Marry, he trots hard with [not "withal"] a young maid between the contract of her marriage and the day it is solemnized"—but I wouldn't count on my readers' understanding that fine point of usage.
If your goal is to sound oldish but not altogether archaic in this poem, I think you might do better with "beside" (in place of "withal"), though you'd have to move it after "wax'd" if you wanted to retain the line's meter:
He wax'd beside in stature great.
...but this maneuver creates complications of its own, since "beside" (as a preposition) meaning "besides" (as a preposition) is modern English, but "beside" (as an adverb) meaning "besides" (as an adverb) is archaic, according to Merriam-Webster's.
If you don't mind sounding up-to-date, you could simply (and clearly) end your original line with "besides" or "as well" in place of "withal."
Best Answer
Consider:
(Webster's Unabridged)
As others have noted in the comments, this meaning works with breathing very well.