There's lots of ways to reverse arguments. You can often reverse argument fallacies too. I'm just going to pick one example: The False Dilemma. It's opposite? Dodging the Dilemma.
To recap The False Dilemma: it's when you make it appear as if there's only two options, when in fact there are more. A famous example is Bush's "You're either with us or against us". Conversely, you can deny a real dilemma exists. Here's Julia Gillard, the Prime Minister of Australia:
We can certainly work with industries to transition to a clean-energy economy and in that clean-energy economy there will be more jobs.
Whatever. She's too afraid to say her policy is not a win-win situation. That yes, the immediate effect of a climate tax is to hurt the economy. That there's no magic way around that. That there's a cost now for a benefit later. That gulp, yes, the cost: jobs. She knows the power of soundbites, and knows what a present the truth would be to the opposition if she didn't spin it. So she's dodging the dilemma. Barack Obama loves this pitch. It is however a standard tool in any respectable politician's toolbox. Whatever policy they want to push will have a downside that their opponents can use to frame the policy as a dilemma. The parry is to Dodge the Dilemma as follows:
My opponents are misleading you that having X means we sacrifice Y... That's a false choice... We can have both X and Y.
Dodging the Dilemma ultimately manifests as Having One's Cake and Eating It Too. Here's Obama:
We don't have to choose between a future of spiraling debt and one where we forfeit our investment in our people and our country.
Like so many real world examples of argument fallacies, this has more than one rolled into a single sentence. You'll have to replace "our investment in" with "some advantages for" to kill the glittering strawman. Now, obviously we do have to forfeit some advantages. Whether that's low taxes or social security benefits, something HAS to suffer*. He's dodging the dilemma.
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* Later in his speech, Obama actually says his plan can succeed by "spending reductions in the tax code", a ridiculous euphemism for raising taxes (Jon Stewart had a field day with it).