In a way that is extremely annoying, frustrating, or insulting; in a manner that provokes irritation.
From 'galling' (adjective) plus the adverbial suffix '-ly', which transforms adjectives into adverbs describing how an action happens or a quality is experienced.
The progression from physical galling (chafing skin) to emotional galling to the adverb 'gallingly' shows how English takes a concrete sensation and transforms it through metaphor into abstract emotional states—language is basically poetry with grammar rules.
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