Comparison to the West
First and foremost you're factual wrong, the study did not just compare the Nordic countries to Arab countries, it included a wide ranging countries form Africa, South America, Asia, and claiming otherwise is bold faced lie.
Comparing is valid form of creating empirical evidence. Why is a comparison on gender inequality anymore invalid than a comparison on GPD, Gini-coefficient, wages, taxation.
Are you opposed to the scientific method of comparative studies?
Arab history and an arab problem:
I honestly can't think of someone who had female sex slaves as the first feminist. That is such basic violation of the basic tenets of equality that we believe in.
Islam has as goes for most Abrahamic religion has a patriarchal makeup that if not outright legitimize women's inferiority does it implicitly by being open to interpretation jf. Quran 4: 34 that has legitimized domestic violence, jf. Quran 4: 24 that has legitimized female sex slaves, jf. Quran 2: 228 that directly states that men have a degree authority over women. It becomes even more problematic when Sahih hadiths are included.
Regardless Islam did confer rights to women, but the problem is that since 20th century because of the succesful feminist movements those rights do not compare to the freedoms and opportunities achieved, and day-dreaming of the glory days pre 20th century does not change that.
And for the record the discussion is how Islam and islamic law is practiced and not how it should be according to your "ideal Islam™" that has never manifested itself and previous islamic societies have not been ideal in a feminist perspective, far from it.