In a way that expresses disapproval or warns someone about something they did wrong.
From admonish (Latin admonere: ad- 'to' + monere 'to warn') + -ing + -ly. The adverbial form evolved to describe the manner of delivering a warning or reprimand.
This word is a linguistic onion with multiple layers—starting from Latin 'monere' (to warn), we get admonish, then admonishing (describing the action), and finally admonishingly (describing how that action is done). It shows how English stacks suffixes to create increasingly specific meanings.
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