Picture someone at a pointing the way — and the arm goes to the wrong road. The still walks, still works hard, and still arrives somewhere. Just not where they needed to be. The word is built exactly like that picture: mis- 'wrongly' plus direct 'to point something somewhere'. So every use of it is a complaint about the aim, never about the amount of work or the quality of it.
可以想成有人站在路口幫你指路，手一伸，指向了錯的那條路。你照樣走、照樣用力，也確實會到某個地方，只是不是你要去的地方。這個字的組成剛好就是這個畫面：mis-（錯）加 direct（把某樣東西指向某處）。所以它的每一種用法，抱怨的都是「方向」，不是做得多不多、好不好。差別只在那隻手是不小心指錯，還是故意指錯。
From the word’s history
From mis- + direct. The packet's etymology tree takes mis- back through Old English mis-, a prefix meaning 'wrongly'.
由 mis-（錯）加 direct（指引）組成；資料裡的字源樹把 mis- 追到古英語的 mis-，意思就是「錯誤地」。所以這個字的字面和用法幾乎重疊：指錯方向。
Wiktionary, "misdirect"
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