if a child gets angry and lashes out when they see a particular image - you don't keep shoving that image in their face with the attitude of 'i'm going to keep showing you this until YOU change your reaction to it!'.....WE in the western world can deal with this and exercise our freedom of speech and expression AND stand up for others at the same time in a MUCH more responsible fashion that doesn't end up playing into the hands of terrorists and the deliberate annihilation of innocent lives.
for one thing, you are equating children and muslims, which isn't very charitable to muslims. Second, if a child has unreasonable reactions to anything, say violently responding to a cartoon, we DO train that out of the child and tell them they are unreasonable.
Third, we are not one entity. You are speaking of the west as if we made collective decisions on these topics. We don't. Some media/people are absolutely out to have reasoned, calculated, well-mannered and thought provoking discussions, and others are out to shock, and some are out to do both. I, personally, do not like to insult people, but I see the importance of satire. So, when I discuss these things with people, I don't just whip out a cartoon, but I see that others might.
The point is muslims, or anyone else, don't have to engage with the cartoons if they don't want. It's that persons right to print them, and it is absolutely not anyone's right to shoot them.
You can still publish drawings. But if you do you need to accept it will increase your risk from loons.
no doubt the publishers knew that there is a risk. But it's our job (everyone's) to tell in no uncertain terms to those people that responding with violence is absolutely unacceptable. Full stop.