It's at life-or-death moments that true feelings show.
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From 高攀龙's Ming-era 《讲义·仁远乎哉章》: 此一转念，是生死关头，千圣都从此做成 - 'this single turn of thought is the life-or-death juncture; every sage was forged here.' Originally a moral-philosophical usage, later general.
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关头 literally means 'gate-top / threshold' - the moment of passing through. 生死关头 = 'the threshold between life and death.' Modern extensions: 紧要关头 (crucial moment), 危急关头 (critical moment).
