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Goat rope is US military slang meaning a chaotic or out-of-control situation.
The basic form is "goat fuck" in the sense of "a goat-fucking event", thence "goat rape" and the euphemistic "goat rope". The participants in a "goat fuck" are pictured as engaged in useless and abnormal activities (such as copulation with animals) rather than in purposeful activity. The basic implications are that the situation has degraded to the point where people are raping goats, something which does not generally occur under ordinary day to day circumstances.