For all the efforts to paint al-Qaeda as a bunch of deranged religious zealots who hate us for our freedoms (and our married gays!), the organization is quite clear on its aims. Khalid Sheik Mohammed, for instance, compares Osama bin Laden to George Washington, demands the independence of the Middle East, and says his aim was always to stop "American foreign policy in our land." Now, that may not be something we're willing to do, but it's not an indecipherable aim. As Fareed Zakaria memorably put it, "Washington has a long habit of painting its enemies 10 feet tall—and crazy."
Doing so allow those in power to utterly ignore the roots of any particular conflict and instead use moments of national chaos to advance their own ideological agenda. For instance: If Americans had really understood that the Middle East has radicalized against us in large part due to our history of meddling and coups, in addition to our perceived bias in the Israel/Palestine conflict, they may have decided that invading Iraq was something less than a wise response. Since they were never given the relevant information to make that judgment -- al-Qaeda hates us for our freedoms! -- that choice never became explicit. And this continues on today: Just about no serious observers believe that Iran wants a bomb to blow up Israel. Many believe they want one to protect themselves from America. But what's sold in the American media is a bullshit rationale of Iranian aggression, rather than a more sober examination of their actual motivations.