Simply put, if you want to understand what the terrorist groups teach about Islam, you have to read the article linked above. Here's a quick excerpt to whet your appetite:
It is vital to grasp that traditional and even mainstream Islamic teaching accepts and promotes violence. Shariah, for example, allows apostates to be killed, permits beating women to discipline them, seeks to subjugate non-Muslims to Islam as dhimmis and justifies declaring war to do so. It exhorts good Muslims to exterminate the Jews before the "end of days." The near deafening silence of the Muslim majority against these barbaric practices is evidence enough that there is something fundamentally wrong.Now you see why I say ya gotta read it.