One way to hold this word: two things were locked together, and now the lock is undone. Gears bite into each other, a hand closes on a sleeve, two forces are in contact — engaged. Disengage takes that join apart. Nothing is broken and nothing is removed; both sides are still there, just no longer connected, and usually the is controlled rather than sudden. Every other use in this word is that same , moved onto people, attention, or opposing sides.
Wiktionary gives disengage as from Middle French desengager, that is dis- plus engage. The prefix dis- undoes what engage did, which is exactly the unhooking picture the modern senses share.
Wiktionary 記錄 disengage 來自中古法文 désengager，也就是 dis- 加上 engage。dis- 的作用是把 engage 做過的事情反過來。engage 是扣上、投入，disengage 就是把那個扣解開。現代各個意思共用的畫面，正好就是這個字面組合。
Wiktionary (kaikki extract, disengage): 'From Middle French désengager ; dis- + engage.'
Three branches
身體與機件的脫開
這一組就是核心畫面本身，看得見也摸得到：齒輪、鎖、被抓住的手。其他意思都是從這裡借畫面出去的。
verb · B2
To move one part of a machine away from another part it was joined to, so that the two stop working together; also used of the part itself coming loose, as when a lock or a system switches off.
脫開、解除（機件）
心思與投入的抽離
把「零件脫鉤」的畫面移到一個人的注意力上。人還在現場，連結卻斷了，這正是它跟「離開」最不同的地方。
verb · B2
To stop taking part in something and stop caring about it, so that your attention and effort go somewhere else. It is used with from: disengage from school, from work, from public life.
抽離、不再投入
對峙雙方解除接觸
一樣是鬆開，只是這次咬在一起的是對立的兩邊。重點在「接觸停止、距離拉開」，不在誰贏。
verb · C1
If two armies or two opposing sides disengage, they stop fighting each other and move apart. A commander can also disengage a unit, meaning they order it to break off and pull back.
脫離接觸、停止交戰
以下是外部詞典記錄的用法，原文照列，我們還沒有寫成教學內容。上面的說明才是我們自己寫的；有些用法可能上面已經講過了。
disengagenoun/ˌdɪsɪŋˈɡeɪd͡ʒ/
fencinggovernmenthobbiesA circular movement of the blade that avoids the opponent's parry
disengageverb/ˌdɪsɪŋˈɡeɪd͡ʒ/
To release or loosen from something that binds, entangles, holds, or interlocks.
資料來源：英文維基詞典 English Wiktionary（CC BY-SA 4.0）。 原文照列，未經改寫。