"Sorry dude, I played G.T.W with your mom and there's no way anyone could be better."
Suspending disbelief temporarily, the concept for debaters is this: no man-made event could be worse than several major world powers choosing to initiate a nuclear exchange. Theoretically, such an exchange could kill most of the life on the planet's surface. Given that, if you can show that there is a chance, however small, that a given plan of action increases the likelihood of nuclear war, then that plan cannot be enacted, regardless of its benefits. This basic logic can be tailored to suit a given topic by exchanging GTW for a more appropriate worst case scenario.
As a sidenote, while GTW may or may not really be a relevant consideration in some topics of debate, certain students relish finding inordinately convoluted paths by which, for example, domestic social policies could lead to the end of the world.
Magnet schools? They'll breed more right-wing hawks, therefore GTW!
National sales tax? They're regressive, will force folks to elect more neoconservative isolationists, therefore GTW!
Take the kids out for pizza? Children are the future; childhood obesity is rising; more sickly children equal more health costs; subsequent failure of the current state health program will lead the masses to request socialist-style health policies, snowballing socialist reforms throughout society; the western free market cannot persist under heavy socialist governance; the West suffers an unprecedented depression; global depression leads to an increase in nationalism, while the new power vacuum draws petty tyrants toward the dream of hegemony; a new fascist state arises, and decides to start ethnic cleansing with a nuclear broom, therefore GTW -- all because someone didn't make Willy eat his green beans.
The truly silly thing is that some number of academic debates get decided by the judge tallying how many GTW-style scenarios survived the round on each side, then handing it to the "lesser of two evils."
More seriously, here's how it goes (sans "evidence" -- read: bullshit).
An (arguably) rational GTW usage I heard awhile back:
Proposed plan: America to assist China to construct modern nuclear reactors, offering deals on fissionable matter and technical know-how.
a) China's nuclear capacity is currently no match for that of the West, in either live weapons or raw materials.
b) Providing nuclear materials could allow China to more quickly upgrade its nuclear capacity.
c) US-China relations are possibly at a tipping point now.
d) Rapid Chinese armament makes a 21st-century arms race likely, threatening GTW.
THEREFORE, America cannot help China build reactors.
A stupid, stupid GTW usage I heard in debate recently:
Proposal: Decrease (American) federal agricultural subsidies.
a) Currently, American agriculture is just barely surviving thanks to increased government-sponsored interest in biofuels. So, cutting subsidies will ruin many farmers.
b) The act of decreasing ag subsidies will increase voter sympathy for neoconservative interest groups in the next election, pushing the country further to the political right.
c) America is standing at the top of a slippery slope leading to severe isolationism; it is just a few right-wing Congressional seats from imposing many xenophobic policies, from protective tariffs to literal wall-building.
d) An immediate and wholehearted embrace of multilateralism is the only way to halt jihad and stop a dangerous Sino-US Cold War.
THEREFORE, America cannot decrease agricultural subsidies.
For more examples of the above, I'd advise you to go volunteer to judge a high-school debate tournament in your community. Then, try to imagine a wad of college kids jabbering (literally) three times as quickly as the high-schoolers and armed with the latest round of bad metaphors and buzzwords they've picked up in a few years of undergrad political science and philosophy courses. Finally, consider that many of our current world leaders "did debate" in college. Scary.