Making the loud call of a rooster, or boasting proudly about an achievement or success.
From Old English 'crawan,' which is imitative in origin—the word sounds like a rooster's call. Transferred to mean loud boasting by the early 1600s.
Roosters crow at dawn because of internal biological clocks, but they also crow competitively—crowing is literally how roosters establish dominance, so when humans crow about achievements, we're channeling ancient animal behavior.
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