I don't care much for AEI -- way too partisan and not very insightful. For example:
Interpreting classical statistics correctly is perilous, and I'm pretty sure that this is wrong.
It also depends on what part of the distribution you are interested in -- in particular, consider the extremes.
(a) It's been fairly well documented that
severe intellectual disabilities are in the neighborhood of 4x - 6x more likely in males. (I can foot to some stuff from The Economist I think.) That alone is enough to spike variance if the means are comparable and we are in fact evaluating the entire distribution (and remember we are talking about squared deviations so variance weights extreme things more). (b) A more interesting test would look at whether the distributions are actually well approximated as symmetric (and in particular whether this holds at the extremes which may not be so easy).
There is a ton of subtlety involved and I've met just about no one who is able to think through these things dispassionately, deal with subtleties and guard against ideological and self-serving biases. As a result, I have a hunch that this is
not appropriate for the forum.
It's worth recalling that the final straw in Larry Summer's presidency at Harvard was speculating on variance in intellect and its potential impact in physics. Edge.org had a very good discussion on superforecasting which at one point remarked that this is viewed merely as hypothesis generation by those small few that qualify as superforecasters and most everyone else went berserk after hearing it.
Come to think of it there is a lot of good stuff in that thing on superforecasting, that is probably a lot more fruitful and interesting to read through:
https://www.edge.org/event/edge-master-class-2015-philip-tetlock-a-short-course-in-superforecasting
(I actually think this 5 part discussion may be better than the book.)