I suspect the only reason we are not taking out Al Jaazera is because they are actually an intelligence function of the U.S. They probably are giving us information about the location of terrorists etc.
The only intelligence I see Al-Jazeera providing us is a bad image. They've done more harm than good and want to be that way to show the arab world that americans are just "infedels" to them. They love the violent culture they have and don't want the west to influence "their way"