Welcome to the concept of a "straw man".
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To "attack a straw man" is to create the illusion of having refuted a proposition by replacing it with a superficially similar yet unequivalent proposition (the "straw man"), and to refute it, without ever having actually refuted the original position. This technique has been used throughout history in polemical debate, particularly in arguments about highly charged, emotional issues.
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http://en.wikipedia.org/wiki/Straw_man