To interpret something wrongly, especially by giving it a meaning that was not intended.
From 'mis-' (wrongly) plus 'construe' from Latin 'construere' meaning 'to build' or 'arrange.' Originally referred to incorrect grammatical parsing, then expanded to any wrong interpretation.
The word literally means 'to build wrongly'! Just as a builder might misread blueprints and construct something incorrectly, we can misread social cues or texts and construct the wrong meaning in our minds.
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