I have some problems with this article. But it's early and I'm distracted so I might end up ranting incoherently.

First off, it doesn't matter if Turkey, Kosovo, and Kyrgystan have secular governments and have had periods of intense religious persecution several decades ago; the populace is still, by a vast majority, Muslim. They're still Muslim majority countries. If the argument is that only governments that actively endorse and enforce religious laws can be considered 'Muslim countries,' then I'd say you've just defined 'Muslim country' to only include extremist governments. Any government that is actively enforcing ANY religion is an extreme form of government. And this brings the problem back to the person/organization practicing Islam as opposed to the problem being with Islam.

As far as gender inequality goes, I don't think anyone is going to deny that gender equality has been a problem in most major civilizations throughout history regardless of religion. If you want to argue about how Islam and gender equality are correlated or causally related, talking about inequality in Muslim majority countries isn't enough. Saying there is gender inequality in Muslim majority countries isn't enough to make any conclusion. How does the gender equality in Malaysia, in Bangladesh, etc. compare to the gender equality of countries nearby, countries with similar geopolitical standing, countries with similar economic and political development?

The same goes for the women as heads of state argument. It's fine and dandy that you can find some mitigating circumstances in a lot of the cases, but does this same nepotism and political pandering not occur in states that aren't Muslim majority?

There are obviously questionable teachings in the Quran. There are questionable teachings in every religious text. The Bible has just as much support for violence and gender inequality as the Quran does. Any government that is going to strictly enforce ANY religion is going to have abuses of human rights, gender inequality, capital punishment, etc. All of these religions came about and reflect a time in which human rights were regularly abused and when authoritarian leadership was normal. The form of change that needs to take place is with society and how it views and incorporates religion, not with religion itself.

Reza Aslan's main point is that a religion is only going to be as peaceful or as violent as the person practicing it or the government enforcing it, and this article, as far as I can tell, does nothing to address either of these points. I think the real way to progress is somewhere between Reza Aslan's views and this article's views. Less strictly apologist than Reza, and a bit more analytically insightful than this rebuttal.

I see all of these negative traits correlated with countries that are largely Muslim, but I also see them correlated with other factors. I see them correlated with authoritarian government, I see them correlated with high levels of economic and political inequality, I see them correlated with countries with long histories of geopolitical instability, I see them correlated with countries that have large, uneducated and culturally isolated rural populations. I think the correlation with religion is the least strong and least causal correlation, just like the correlation between race and criminality here in the US. There's more crime committed by black people than by white people, there are more black people in prisons, but the correlation between criminality and socioeconomic factors are stronger and are causal, and focusing on the correlation between race and criminality just obscures the point.