Canadian Cynic (whose choice of language often pisses me off, but whose opinions I generally agree with) posted this gem about arguing with conservatives It's sheer genius.
I've noticed that some liberals argue like that too, but not as many, IME.
Also, IME, it seems to be people who don't know their facts well who do this. They do it to cover that they can't make the argument, but aren't willing to change their opinions or admit they were wrong. Or even, they still don't believe they're wrong (and maybe they aren't), but simply don't have the argument to back it up.
Slightly tangentially, I was arguing with someone on a vegan board I frequent (I'm not vegan, but close enough that the recipes there are useful to me). Anyway, she was going on about how Coke is terrible for your health. Yes, correct, I agree with your statement. However, she was going on about how you can pour a Coke in a toilet and then clean with it, and was using that as "proof" that Coke is bad for you. I hate that. My insides are not a toilet. My gut is not porcelain. This ridiculous analogy fails, and makes the arguer look stupid. So, because I am no good at just letting things go, I said, "Oh, look what water does to pipes! And the water damage in my wall is considerable. Water must be bad for me too!" She totally didn't get it. She got mad at me, first for saying that Coke is good for you (um, nope, didn't say that, I said her conclusion wasn't supported by her premises, but that I didn't for the first minute deny the conclusion), then for suggesting that water is bad for you (um... miss the point much?), and then for being so stupid I didn't realize that my body isn't copper piping (*sigh*). Finally, I just said, "Listen to me. I'm trying to help you make your point better. Faulty logic isn't going to help you." So now she hates me, but I really don't care. :)
I think faulty logic might just be my biggest pet peeve.