Straw man. This is the fallacy of refuting a caricatured or extreme version of somebody's argument, rather than the actual argument they've made. Often this fallacy involves putting words into somebody's mouth by saying they've made arguments they haven't actually made, in which case the straw man argument is a veiled version of argumentum ad logicam. One example of a straw man argument would be to say, "Mr. Jones thinks that capitalism is good because everybody earns whatever wealth they have, but this is clearly false because many people just inherit their fortunes," when in fact Mr. Jones had not made the "earnings" argument and had instead argued, say, that capitalism gives most people an incentive to work and save. The fact that some arguments made for a policy are wrong does not imply that the policy itself is wrong.
In debate, strategic use of a straw man can be very effective. A carefully constructed straw man can sometimes entice an unsuspecting opponent into defending a silly argument that he would not have tried to defend otherwise. But this strategy only works if the straw man is not too different from the arguments your opponent has actually made, because a really outrageous straw man will be recognized as just that. The best straw man is not, in fact, a fallacy at all, but simply a logical extension or amplification of an argument your opponent has made.