Nice "wisdom" there. But why did you stop thinking there? There IS definitely a link between excessive testosterone and the lowering of sustained logic, reason and mental stability and order. (Just as there is similar evidence liking excessive estrogen with similar behaviors among women) What happens to people, both men and women when they are on steroids? That's been well established in the medical sciences for decades.
So to say correlation/causation is a problem here conveniently missed the established facts and among these the effect of higher testosterone on mental capacity.
I think the recognition of corre-cause fundamental principle is an important aspect of reasoning. But it is not the whole of debunking anything. (And yes, nothing you say disagrees with that statement.) But to simply state "correlation != causation" and walk away as if you've debunked something is pretty commonly expressed in these parts and I find it disturbing.
We're bio-chemical machines. The efficacy of the machines has everything to do with what's in them, what the balances are and especially what we put into them. But even if that balance is essentially natural or origin and basis, the outcome is still an effect of the factors at play. That is to say, groups of people with higher levels than others show predictable results categorically speaking. (But that's "racist" and we're not allowed to talk about that either)
If anything, this "finding" is just another grain of evidence supporting the obvious where human evolution are concerned. As we continue to value intellectual ability over physical ability, those who have better intellectual ability will do better than those that do not. And for societies to evolve in a direction which favors mind power over physical power literally requires and causes a reduction in that which inhibits it the most. Think in terms of rust causing heat which causes more rust and it's not so much corre-cause as it is factors feeding into one another.
No, I don't favor the "men are obsolete" argument as it's ridiculous on its face. Feminism, like so many other hate-focused idealisms, requires an enemy. And the biggest problem with feminism's enemy is that they are the ones who create and maintain pretty much everything. That's why all of the push for "more women in these fields." The push is because as men continue to become disenfranchised, they know there is a need to replace them. The problem is they don't have anyone who WANTS to replace them because cetegorically speaking, women are interested in what women are interested in while men are interested in what interests men. And there's a certain amount of "nature" driving this fact. Deviations are fine and welcome, but attempting to force idealism over nature has NEVER worked in all of history for any sustainable amount of time and has never resulted in happiness, peace or harmony. So let's not take the observation and the apparent conclusions into political space.
Men cannot be obsolete if only because we are half of that biological basis of sustainable reproduction, development and adaptation. We need to be able to breed and cross-breed as a means of continuation. And that requires men and women... until they can effectively create artificial sperm... which yes, I know they're working on even now.