To fail to achieve the intended goal or to be inaccurate; to not succeed in what one was trying to accomplish.
This phrase originates from archery and other target sports, where 'the mark' was the target one aimed for. Missing the mark meant your arrow or projectile failed to hit its intended destination. The metaphorical use developed in the 16th century.
Archery metaphors are surprisingly common in English because the sport was so central to medieval life and warfare. What's interesting about 'miss the mark' is that it implies the attempt was reasonable but the execution was flawed - unlike 'wide of the mark,' which suggests being completely wrong from the start.
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