Because the "belief system" is a murdering death cult, and needs to be eradicated. Humiliate them and treat them like Nazis, who also sought to kill or enslave everyone else.
So your strategy would be:
Why go after thousands of extremists when we can pick a fight with 1.3 billion people all at once?
Good strategy.
PS: I'm for free speech. I support the Danish cartoons and those who want to print them. I just think the State Dept also is making a valid point here. So go ahead: Flame On!