I think the most maddening of all of the logical fallacies is the Straw Man.
In case you're not familiar with this particular infuriating ploy, the Straw Man fallacy is when the individual you're arguing with knocks down an oversimplified (or exaggerated, or flat-out incorrect) characterization of your position, and then forthwith declares that (s)he has won the argument. Ann Coulter, that living embodiment of specious thinking, is the past master of the Straw Man; she is notorious for taking the weakest (or most extreme) viewpoints of American liberals, demonstrating that those are incorrect, and concluding from this that all Democrats (i.e. around 50% of Americans) are blithering morons.
But you've never seen an example of the Straw Man fallacy like the one I'm about to show you.
Zach Kopplin, a young man from my home state of Louisiana who has become a champion for the teaching of evolutionary biology in public school science classes, posted a video on YouTube, showing a discussion between Louisiana Senator Mike Walsworth and a high school science teacher on the floor of the state senate. Walsworth asks the teacher if there are any experiments that have been done that demonstrate Darwinian evolution in action. The teacher responds that there have, and proceeds to describe Richard Lenski's elegant experiment with the bacteria E. coli, in which a population of E. coli were sampled over decades, and the samples frozen, with the (unfrozen) remainder subjected to various environmental factors as selecting agents -- and at the end of the decades-long project, all of the bacteria, the various frozen ones and the ones that had been allowed to continue growing, were compared. (Estimates are that in the duration of the experiment, over 50,000 generations of bacteria had occurred.) Guess what? The lineage had changed demonstrably, with novel genes cropping up (including one that allowed one branch of the "family" to metabolize citric acid). There you are: evolution in action.
And then Senator Walsworth asked the teacher if any of the bacteria had evolved into a human. (It may have been my imagination that immediately afterward, Senator Walsworth added, "Herp derp hurr!")
The teacher, of course, responded "No." And one lady in the audience did a highly amusing forehead-smack. But you could just about hear all of the creationists in the audience responding, "Well, ha! There you go, then! I guess Senator Walsworth showed you."
You'd think that the transparency of this particular Straw Man would be so obvious that no one could possibly fall for it. But this sort of response is frequent enough that you have to wonder if creationists attend special Straw Man Training Workshops in order to learn how to perform it as obnoxiously as possible. I've had conversations with creationists (I won't dignify them with the name "arguments"), and have been asked questions like, "Have you ever seen a cat give birth to a squid? Well, okay, then! (Herp derp hurr.)" You can trot out all of the evidence you want, all of the examples of evolution being directly observed in the field or in the lab, but if you can't show me an animal evolving, in one generation, into an animal from a whole different freakin' phylum, I'm not buying it.
But of course, that last statement is the crux of the matter, isn't it? "I'm not buying it." I've already decided what I believe (note, "believe;" not "understand"). Nothing you can do can change that. If you establish your definitions and evidence, I'll just shift my ground so that it redefines the terms. (Yet another fallacy, the "No True Scotsman" fallacy.) Show me experiments that support your theory, I'll ask why those experiments didn't do something entirely different, and then sit back with a cheesy grin on my face and claim I won.
The sad fact is, by some estimates 30% of Americans do think that this constitutes "winning." And you may think this is a tad harsh, but it's my considered opinion that anyone who is that incapable of understanding the basics of critical thinking (not to mention the basics of biology, chemistry, and scientific induction) should not be entrusted to cast a vote.
Which, now that I come to think of it, explains Mike Walsworth's presence in the Louisiana senate.