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Adjective: unconvincing  ,ún-kun'vin-sing
  1. Not convincing
    "as unconvincing as a forced smile"; "unconvincing argument";
    - flimsy
  2. Having a probability too low to inspire belief
    - improbable, unbelievable, unlikely, doubtful

See also: implausible, incredible, unbelievable, unpersuasive

Antonym: convincing