I understand the arguments of those who support building the mosque. They say that most Muslims are not at war with the West in general and the U.S. in particular. I will grant that the current behavior of most Muslims supports this view. I am much less certain about where their sympathies lie.
On the other hand, there is no doubt that the atrocities of 9/11 were committed in the name of Islam. The terrorists were Saudis and others who believed they were dying for Islam.
Is there any doubt that al Qaeda would view the building of a mosque in this location as a victory? That the suicide terrorists responsible for 9/11 would view it as a victory? Of course not.
This is a large country, there are many places where a mosque can be built. Building one at the site of a murderous terrorist act committed in the name of Islam is abhorrent. It says to our declared enemy, "I am weak, I can be defeated."