I am not going to second-guess this reader's experience. But I would say that, from what I know, Islam is not monolithic and has many strains and sub-varieties that will inevitably affect its capacity to adapt to modernity. I can also think of two predominantly Muslim countries that don't support this argument: Indonesia and Malaysia. But that Islam does indeed have a problem I'm afraid I no longer doubt. "Problem" may even be too euphemistic a word. Pathology in some places is more appropriate.
I'll give Mr. Sullivan credit, "pathology" is much more meet than "problem".