I've always failed to understand the hate that drives these people. I try to imagine what kind of hate i'd have to possess to allow me to behead someone while they are alive... The most aggravating thing I can think of is someone harming a helpless woman (sister, wife, mother)... Even then, I don't think I could behead them while they were alive.
Well, I'd say there are two big factors. First off, you have to consider that a good majority of these extremists are extremely poorly educated (as in nothing past elementary school or possibly middle school) whereas the people who are directing them (i.e. OBL) and concocting these operations are not only educated but very calculating. These people are easy to brain wash and easy to fill with emotionally, religiously-charged rhetoric because they simply have never been forced or even encouraged to think for themselves. Ever.
Next, these people very much view the US and anyone - even Muslims - who are not entirely ideologically-aligned with them as the absolute anti-Christ, if you will, and - again, this harks back to the brainwashing bit - are absolutely set in their ways and convinced that what they are doing will ultimately be rewarded in martyrdom. Also, the fact that they may or may not have directly lost multiple family members over the course of the conflict over there in these last few years surely exacerbates the situation immensely.