A less obvious problem for the Muslim argument is that science has been smothered in Islamic countries. While individual Muslims have made scientific progress (there were brilliant medieval Muslim doctors and engineers, for instance), Islamic civilization has never come close to experiencing what we might call a "scientific revolution." This would be an odd fact if the Qur'an were a book full of scientific insights that couldn't be verified until centuries later.
The reality is that the scientific revolution occurred among people who believed that they were created in the image of God and that they could therefore understand God's creation. This belief doesn't exist in Islam. That's why science exploded in the Christian West.