Reluctant or unwilling; lacking desire to do something.
From disincline (past participle used as adjective). The adjective form of the verb disincline, created by treating the past participle as an adjective to describe someone's state of reluctance or unwillingness.
This adjective is far more common than the verb form 'disincline,' suggesting that English speakers mostly use it to describe states rather than to describe causing unwillingness. 'I am disinclined' became a polite, understated way to refuse something—far more subtle than 'I don't want to.'
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