To be very angry and upset, or literally to produce smoke or vapor.
From Latin 'fumare,' meaning 'to smoke' or 'to steam.' The literal meaning (producing fumes) came first, then metaphorically people who were 'fuming' were compared to something emitting smoke from anger.
This is a perfect example of how English borrows metaphors from physical reality—we say someone is 'fuming,' 'burning with anger,' or 'boiling mad,' which shows how emotions get compared to heat, steam, and combustion across many languages.
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