It goes round and round. Islam gets insulted and something or someone Western gets attacked.
Insert another attempt to be even-handed [here] and another 'this is not Islam' [here]. I have no interest in excusing Islam, if only because I'm no expert on Islam. But I'd like to suggest one apparently unnoticed Western contribution to this sorry dynamic. It has to do with misunderstandings about free speech.
Free speech is a peculiarly Western value, which is probably why the West has advanced capacities to reject it. To understand what it is, is to understand why the world, including the West, hates it.
First, free speech is not a democratic value. It is an antidemocratic value, memorably promoted by John Stuart Mill to protect unpopular minority opinions against the majority - that is, against the will of the people. America's élite founders, steeped in the ideals of the French Enlightenment, embedded the right to free speech in the US Constitution. Much as I hate to praise anything American, I have to say that this ideal has been, more or less, preserved in the US, and it is probably the most genuine element of the largely phony ideal of American freedom. To those who don't get it: in the US, hate speech is legal. Insults to religion or the government or the army or the majesty of the nation or anything else are legal. The limits of free speech are set, reasonably, according to the effects of the speech, not according to its content. Words which might be innocuous in one context might be forbidden in another - for instance, if they incite to riot. or tend to provoke armed rebellion, or certain lesser crimes. Whether the content of the speech is insulting, or hateful, has no bearing on the matter.
So how is it that the West, largely under American influence, is complicit in the cycle of insult and retaliation that seems only to intensify with time? It has to do with hate speech laws.
There are no such laws in the US, but Americans really hate free speech. Because most unpopular speech is protected by law, it is pilloried by other means. Americans, incapable of solving their social problems, have gone after something that seemed more manageable - language. Companies, schools, universities, all have policies against hate speech. This is just an extension of 'political correctness', which holds that (1) what you call members of a race, sex, or disability group determines your moral character , (2) if enough people avoid these wrong expressions, they will have a better character, acquire the right attitudes, treat one another well, and then (3) social problems will disappear. Or something like that.
Other Western countries, which never really understood free speech in the first place, don't need to use social pressure to restrict it. They have passed numerous hate speech laws. This works better, of course: you really do have to watch what you say.
Hate speech laws are expansionary. While I might 'commit' hate speech by saying I hate you, maybe I won't be so explicit. Maybe I'll just insult you, or mock you, or say something not nice about something obviously dear to you. Any of this will do in prosecutions for hate speech. This has made the laws a tool and an inspiration, not only for fanatics, but for moderates who, well, don't like to be offended, or even who don't like others to be offended.
Muslims of all sorts read the news. They know about these laws. Even nominal Muslims, virtual secularists, approve of them - after all, aren't we all against hate? This means that fanatics can count on a good deal of very moderate Islamist support. As a web search will show, it is not only the fanatics who have been using these laws to attack real or perceived insults to Islam since well before the Danish cartoons affair.
The West shares responsibility for the current tragicomedy because it no longer believes in protecting speech it dislikes. In the US, this becomes apparent when judges dare to protect unpopular opinions - witness, for example, the majority's outrage at anyone questioning orthodoxies about pedophilia. Indeed the West never feels so moral as when it yearns to withhold this protection or when, outside the US, it actually does so. So Islamists of all persuasions can reasonably ask: "if the West deplores protecting speech it dislikes, why shouldn't we do the same? After all, we're not held back by some creaky American constitution that annoys even the Americans! Why shouldn't laws regarding speech follow the democratic will of the people, rather than the will of a few 18th and 19th Century liberals? Why should we value free speech more than the Europeans, who don't seem to value it at all?"
They have a point. You can reproach Islamists as much as you like, but acknowledge that, where free speech is concerned, they Share Our Values, that is, they hate it. Genuinely espousing ideals of free speech probably won't improve matters. But if matters have any chance of improving, that's a necessary first step.