Imagine a hypothetical YouTube where the videographer burns a Koran and urinates on the ashes. We in the modern West consider this kind of thing an act of free speech.
Would that act be offensive to Muslims? Absolutely. It be offensive to Jews if it were a Torah. It would be offensive to Christians if it were a Bible. It would be offensive to United States patriots if it were the Constitution.
Do Jews, Christians, or United States patriots use that kind of speech as a pretext to riot or murder? If so, would their violence be met with sympathy from the West? No, no, and no. Burning a Koran, and reactions thereto, should be no different.
But here's the thing: you feel *safe* when you criticize Jews, Christians, and United States patriots, because you know they don't consider it acceptable to do violence in response to offensive speech. You *don't* feel safe when it comes to Muslims, because you know there is a non-trivial number of them who *do* consider it acceptable, even a requirement, to do violence in response to offensive speech.
The vast majority of Muslims reading this are civilized, and recognize that violence is not a civilized response to offensive speech. But there are some Muslims, and their sympathizers, who believe that offensive speech must be answered with violence, and who will use offensive speech as a pretext for riot and murder. The behavior is uncivilized, premodern, and barbaric, and should be recognized as such.