To disengage means to "free or disentangle" yourself or some object from another person or object. No, it doesn't mean breaking off your engagement to your beloved — that's "chickening out."

Does your mind wander when someone (your fiancé, for example) talks to you? Well, your mind can disengage as well, that is, stop paying attention. Disengage has quite a formal, intellectual ring to it, even if used about a situation as physical as two armies "disengaging from combat." It's a technical term, and faintly clinical; the kind of word frequently used by politicians and diplomats.

Definitions of disengage
  1. verb
    release from something that holds fast, connects, or entangles
    “I want to disengage myself from his influence”
    disengage the gears”
    synonyms: withdraw
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    engage, lock, mesh, operate
    keep engaged
    set free or release
    type of:
    let go, let go of, release, relinquish
    release, as from one's grip
  2. verb
    free or remove obstruction from
    synonyms: free
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    block, close up, impede, jam, obstruct, obturate, occlude
    block passage through
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    dig out
    dig out from underneath earth or snow
    become or cause to become unobstructed
    loosen up, unstuff
    cause to become unblocked
    disencumber, disentangle, extricate, untangle
    release from entanglement of difficulty
    clear or remove an obstruction from
  3. verb
    become free
    “in neutral, the gears disengage
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    get caught
    become unlocked
    disengage the clutch of a car
    type of:
    change state, turn
    undergo a transformation or a change of position or action
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