"Muslims consider it offensive to show Mohammed, and the cartoons were actually insulting even if they didn't. Don't you think Muslims had a reason to be insulted?"
1) Yes. Muslims had a reason to be insulted.
2) Non-Muslims are not bound by Muslim law, and can post any cartoon they please, including Mohammed's face, if they want to. It may not be wise, it may not be considerate, but they are allowed.
3) Muslims have every right to express anger when they do so. Or to boycott. Or to protest. Whatever. They do NOT have the right to threaten violence. That's crap.
4) I have no idea why the U.S. decided to stick its nose into a religion/free speech conflict between the nation of Denmark and the Muslim religion. That was just stupid.
Hope that clears that up.