Dalena:
I do not know the origin of the phrase, but you can think of it this way.
If there was dog poop to clean up from the ground, and one end of the stick had dog poop on it, that end would be the wrong end to touch.
Therefore, any time you get the worst or unpleasant part of any experience, you can use the phrase "get the wrong end of the stick" to figuratively describe your experience.
For example, you might say; "You know, I dated that young man, and he was nice at first; but he was manipulative, and I really got the wrong end of the stick in that brief relationship."
. (Hope that helps.)
Or, how about an athletic competition? "The way the referee was calling the penalties in that soccer game, our team really got the wrong end of the stick!"
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we really got the