I would argue that like many other intellectual trends, the idea of gender being a social construct is because of attempting to pigeon-hole some things in a way that makes it socially acceptable. But the REAL error is that one size fits all. It is the very ATTEMPT to pigeonhole people that is the error.
In other posts I have alluded to studies that suggest that the human brain has multiple configurations and that one can either assign them as "normally found in men" or "normally found in women." I am not a brain morphologist and therefore cannot tell you any details, but I'll remind you of where to look. Do a search for "homosexual + brain scan" and watch for U.K. medical research articles starting in the 1990s using Positron Emission Tomography (a.k.a. PET scans) to identify brain structure. Research has continued using other radiological methods through at least Sweden in the 2000-2010 range. They lead to a sure conclusion - that Lady Gaga got it right. For homosexuality, you were born that way.
The short answer is that when a person has a "normally female" configuration in a body with male secondary sex characteristics such as male genitalia, muscle mass, and lots of hair, you have extremely good odds of the person being gay. Ditto, "normally male" in a body with female secondary sex characteristics including breasts and less body hair.
The question about "nature vs. nurture" pops up again because sometimes there IS no childhood trauma, no parental neglect, no bad dream, no "nurture" source for someone identifying as gay. When you have mixed signals between the brain and the secondary sex organs, the brain ALWAYS wins because it is THE most powerful sex organ in the body. You go where your brain points you.
The person writing the referenced article is to be commended. It takes a lot of guts and a lot of introspection to be able to recognize that you wrote a pile of dyspeptic dragon droppings and bamboozled people into thinking you knew anything. And a lot more guts to admit it. And even more to admit it was all hogwash.
Here is my opinion. Sex is a biological construct. Sexual behavior (perceived gender) is a product of both nature and nurture. Gender-oriented clothing is obviously cultural. Gender-oriented behavior has at least a serious component of biology.
If you observe a true lesbian relationship, you will always find one partner is the sexual aggressor and the other is more passive. At least, every time I've seen that kind of relation, it was that way. I have seen fewer homosexual male couples but the few that I have seen tend to not be symmetrical either.
In case anyone is unsure of why I take this stance, as it happens I have a gay step-daughter who is married to her same-sex partner. I have had many gay friends from my college days and knew a few gay folks from my Dungeons and Dragons days (the "sit around, eat pizza, roll dice, and IMAGINE your surroundings" version of that game.) Not even using a board for reference of location. I learned long ago that there is nothing wrong with gay people except other peoples expectations thereof. And THERE is where the "social construct" comes into play.
Just so we get it clear, there ARE people in this world who take gender identity blurring a bit farther than others. Case in point: