Do you really think that the terrorists think that they are going to persuade or coerce those they are opposed to to their way of thinking? Of course not.
Their goal is not to persuade anybody. Their goal is to cause as much fucking mayhem as they can, and gain brownie points in heaven for doing so.
Uh, hate to disturb your fantasy, but you should read some history: most terrorists have concrete political goals in mind, no matter how wacky they may seem to you. Some of their actions are completely ineffective at coercion (e.g. Tim McVeigh). Beginning with Ireland and continuing throughout the 20th C., however, terrorism has, in general, been extremely effective at persuading colonial powers (or at least nominally democratic ones) that it is not worth the price to stay in the country occupied. The exception to this rule is where the occupiers feel like the land is, or should be, part of their country (e.g. Palestine, Chechnya), and are willing to accept high casualties in order to remain.
With regard to Al Qaeda, one of their stated goals is to get all Western powers out of the Middle East, and in particular, to get US bases out of Saudi Arabia; the fact that the US is, in fact, removing its bases from Saudi Arabia can be attributed in part to Al Qaeda's influence.
