Arrogant, conceited, or having an exaggerated sense of one's own importance; also literally having a disproportionately large head.
Compound adjective from 'big' + 'headed'. The metaphorical use (meaning arrogant) emerged because humans psychologically associate head size with intelligence and power, making it a natural source for arrogance metaphors.
Every culture that speaks about arrogance seems to reference the head—'bigheaded' in English, 'grosse tête' in French, 'cabezudo' in Spanish. This suggests something deep about how humans physically express arrogance—literal head-holding posture perhaps influenced centuries of metaphor-making.
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