Essentially, he finds what peeves Muslims is our insistence that religion be a private matter, not the basis of government. They want to base their government on the tenets of Islam.
Muslims are offended that we see this as theocracy, old-fashioned, what we did centuries ago. There is more to the issue but U.S. support for those elements in their societies which want the state to be secular is repellent to many of them.
It is a long article, and possibly wrong to boot, but it does explain some facts on the ground.