Think of an earphone cable that has been loose in a bag all week. The line only touched itself at first, but every movement wound it a little tighter, and now pulling one end makes the knot worse. That is the whole word: something long wraps around something else and holds it, and the way out is not the way in. English then lends that picture out. A person who agreed to one small favour and cannot now get their name off the papers is in an entanglement. Wire strung in front of a position is an entanglement, because catching and holding is its job. And borrowed it for two particles that can no longer be described one at a time.
Wiktionary gives it as entangle + -ment: the verb entangle plus the ending that turns an action into a thing. Entangle itself is en- (make into) plus tangle, so the word starts life meaning the act or result of being wound into a tangle.
Wiktionary 記載這個字是 entangle 加上字尾 -ment：-ment 把動作變成名詞。entangle 本身是 en-（使進入）加上 tangle（一團纏在一起的線）。所以這個字從一開始就是「被繞進一團線裡這件事，或是被繞住的結果」。今天的每一個意思，都還看得到這條線索。
Wiktionary, entry 'entanglement', etymology tree (entangle + -ment), packet evidence kaikki:3f6f69a190036ae4:1242708933
From the picture
人與事情的糾葛
把「被線繞住、越拉越緊」整張圖搬到人身上。差別只在纏住你的不是繩子，而是感情、金錢、法律或政治。所以這個意思一定帶著「麻煩、脫不了身」的味道，也才會常常跟 avoid 一起出現。
noun · C1
A relationship or situation that you have become caught up in and cannot easily get out of, usually one that brings you trouble or takes away some of your freedom.
糾葛、牽扯
用來纏住人的障礙
這一支不是被動地被纏住，而是反過來：有人故意做出一個會纏住別人的東西。畫面還是那團繞來繞去的線，只是換成鐵絲，而且是刻意架設的。
noun · C1
A barrier made of barbed wire, put up in front of a position so that soldiers on the other side cannot get close. It is usually spoken of in the plural: entanglements.
鐵絲網障礙
物理上的糾纏
物理學家借的是「兩樣東西纏在一起，沒辦法分開處理」這個感覺，不是真的打結。這是比喻的借用，不是歷史上的另一條來源；中文譯成「量子糾纏」，用的也是同一個比喻。
noun · C1
In physics, a link between two very small particles which makes them behave as one system, so that what you find out about one tells you something about the other, however far apart they are. It is the short form of quantum entanglement.
量子糾纏
noun · C1
The act of becoming twisted and caught in something such as a net, a rope, a wire or branches, or the state of being caught in that way.
纏住、纏繞