Because it doesn't.
There are Muslim members of this board who hold the same patriotic and conservative political views as you. Yet, they would consider themselves "subjects of Islam".
Worldwide, such Muslims are clearly a minority -- perhaps no more than 10% of Islam's billion-and-a-half constituency. Similarly, the Islamofascists are also a minority within Islam -- probably no bigger than a minority than those who value freedom and democratic institutions.
The remaining 80% represent the Islamic equivalent of what some on this board refer to as the "sheeple". While a much larger segment of society than in the U.S., in Islam, as in the U.S., that means uninformed and largely ignorant -- neither a committed libertarian nor necessarily a radical.
These Islamic "sheeple" are "up for grabs". Bin Laden understands this -- recall his "stronger horse" analogy? And so do Bush and Blair -- who have carefully avoided making war on Islam or the national populations. Instead, they have made war rather specifically on a.) the Taliban and then b.) Saddam Hussein.
That this approach can achieve success is obvious: Electoral participation in Iraq (and Afghanistan) topped 70%. The "sheeple" who are "up for grabs" responded to the opportunity.
Why make enemies of a billion-and-half Muslims when you don't have to in order to win?
Because they have already decided we are the enemy.