The idea that al-Qaeda and other Islamic "terrorist" groups are beyond reasoning with is absurd. The "Western" world, and the United States in particular, needs to open a dialogue with al-Qaeda and the worldwide Muslim population as a whole if there is ever to be a peaceful end to the current conflict. Otherwise, people on both sides will continue to act like bloodthirsty animals. Take a look at the Israeli-Palestinian conflict to see what happens when one side or both sides of a hostile situation refuse to negotiate or even regard each other as human beings—generation after generation of violence and hatred.
Many members of so-called terrorist groups are motivated primarily by losses they have suffered at the hands of the people they wish to harm. For example, Usama bin Laden explicitly traced his genesis as a jihadi to the 1982 destruction of Beirut by American and Israeli forces. Ask each jihadi what his or her catalyst is, and you are likely to end up hearing the same things over and over again: "My family was killed in a U.S. firebombing," "I was tortured by American spies," "My hometown was reduced to rubble by Israeli tanks," etc.
People think of Sept. 11, 2001 as a horrible day in American history, and it is, but other countries have suffered far worse fates as a direct result of American military strikes and international economic sanctions. More than ten times as many civilians have been killed in Iraq as were killed on Sept. 11, and the physical damage to that country has been a great deal more serious than a handful of collapsed skyscrapers and some downed aircraft. Consider that, and then proceed to consider that the United States has caused this kind of damage in several other countries in the region. America is also responsible for funding the military machine of Israel, which has killed thousands of Palestinians and other Arabs in the past few decades, most of whom were just ordinary people walking home from work or buying groceries.
Killing innocent people around the world gives survivors a reason to fight back, especially if the conflict is ongoing. The result of decades of violent foreign policy is that a lot of people are going to hate the aggressor. An unwillingness to negotiate with or even talk to the other side only encourages them to take the same position and to regard your side as an inhumane monster hell-bent on murdering everyone. That's how al-Qaeda and Hamas and Hezbollah see America and Israel. If we were more willing to talk, that might change and peace might be possible.
And "talking" does not mean shouting a list of commands from atop the United Nations building with threats of sanctions for non-compliance. The "Western" world must also be willing to make compromises.