What does it exactly mean, our way of life? I would think it refers to certain standards and morals that are upheld in a society. Importantly, these standards are arrived at through years and years of experience, they don't come in a handbook. In the States, way of life is largely directed by what people want to do and how they want to express themselves. I suppose that comes under the broad umbrella of freedom. But what if people want to live in a more structured society? Is their right to pursue such a society less valid than Americans' desire for no-holds-barred type of approach?
I personally don't support what the Taliban perpetrated in Afghanistan, nor what Saddam Hussein did in Iraq.. nor what the Saudi family has constructed in the Arab peninsula - these societies were/are based on fear and suppression. But why do Americans think that all women want to work? That all women want to wear as little as possible? Personally, I don't want to work long-term. I really believe my husband, insh'Allah should provide for our family should we be so fortunate. Part of that is based on my belief on how a family should be structured. Any biology book will show you that men and women are different.
This is going off-topic. My point is, who should decide how different people should live - how they should structure their way of life? In the States, the status quo is constantly being challenged and, as a result, is constantly evolving. The current debate over gay marriages is an example. In the Middle East, there are different norms and historical legacies which have shaped the contemporary cultures of the region. While it is not unreasonable to assume that democracy and freedom and fundamental rights are universal goals, it is important to understand that they can be expressed in a variety of ways. The only way these ideals can possibly be recognized in any real sense is if they are developed from within the socio-cultural context. This can only happen if the governing forces and their mukhabarat are dampened. It is such an ignorant notion to think that people don't want what Americans have but equally ignorant to think that they want everything the way Americans have it.
So maybe it's not so much 'they hate our way of life' but more like 'they just want to live their way of life'.