One of the most maddening aspects of arguing with imbeciles is their lack of understanding of the most basic rules of logic, like the ones explained here. If you've been a regular reader of this blog, you've most likely seen almost all of those rules violated painfully at one time or another.
Consider one of my favourites, the "No True Scotsman ..." fallacy:
Suppose I assert that no Scotsman puts sugar on his porridge. You counter this by pointing out that your friend Angus likes sugar with his porridge. I then say "Ah, yes, but no true Scotsman puts sugar on his porridge.
This is an example of an ad hoc change being used to shore up an assertion, combined with an attempt to shift the meaning of the words used in the original assertion; you might call it a combination of fallacies.
And if you change a few words around, well, it sure looks familiar, doesn't it?
WB: Tom DeLay is going to Rome as part of the U.S. delegation.
CC: Um, no, the U.S. delegation consists of five people, none of which is Tom DeLay.
WB: Well, he's going as part of an unofficial delegation.
Man, I could teach an entire course in critical thinking based on Weasel Boy's stupidity alone, but that's not the point here.
There's one argument I've seen countless times that I don't think has a Latin name. I call it the "Argument from Personal Bewilderment," where the arguer's position is, simply, that because he doesn't understand something, it is therefore not understandable and should be rejected.
You run into this all the time debating with creationists, when they say something like, "Well, I just don't see how your naturalistic, materialistic processes can result in evolution. It just doesn't seem possible, so I don't believe it."
At this point, the proper response is not to try to explain biological evolution even further. The proper response would be to point out that, gosh, that's too bad but science in general and biological evolution in particular doesn't give a rat's ass what he believes. It may be cruel but science marches on -- it doesn't hang around, waiting for some moron's stamp of approval. Said moron probably doesn't understand superconductivity, or cosmology, or general relativity either but, gee, that's tough.
So to the common conservative lament of, "Well, I just don't understand how that can work and I don't believe it," the proper response is, generally, "No one gives a shit what you believe. Deal with it."