I am assuming that by “social construct” we mean how we think about gender, or how we assign gender?
As a social scientist who is very interested in how things are categorized, I know there is a hierarchy of categorization schemes. The most basic is either/or (binary) systems. As people get more sophisticated, they can develop more categories for whatever it is they are categorizing.
For example, you might start with the concept of friend or enemy. Then, as you grow more sophisticated, you might say friend, companion, acquaintance, colleague, persona non grata, enemy. I’m sure there could be several other categories thrown in there, as well.
There is a natural scientific process to the creation of more and more sophisticated categorization schemes. Typically, you do start binary. However, there is one other essential component to categorization efforts. You have to decide what attribute of the thing you want to categorize you will look at. Take a set of pebbles for example. They have different sizes, different colors, different textures, and on and on. If I told you to categorize a pile of pebbles; which attribute of pebbles would you use to divide them into categories. If you used color, where would you draw the line between categories?
Humans try to use categorization systems to predict the behavior of the things they are studying. We first develop a system, but then, in using it, we find anomalies, and we study them, and realize that our initial model could be improved if we add more categories or categorize the objects based on a different attribute.
As a general rule, we usually categorize things into between 2 and 8 categories. There is a biological reason for this having to do with how many different names we can hold in our heads at the same time. The less educated or sophisticated or intelligent you are, the fewer categories you will see.
Simple categorization happens with gender. We start with male and female, usually based on a combination of three attributes humans have: genes, physical form, or who they prefer to love. Then we discover there are people with both genes and both body parts, so what do we do with them? Maybe we create a new name for them. Then we discover there are people who prefer to have love relationships with members of their own sex. What do we do with them? Let’s make up some new names. Then there are people who change sexes; what do we call them? And on and on. I’m sure there are more categories that I haven’t even thought about.
Categorization is always a “social” construct. Look at flora and fauna, a binary category. We accept it as natural that there should be two categories, but someone had to come up with that scheme in the first place. Now we don’t even think about it. Within flora, we have trees, grasses, bushes, etc, etc, We define these categories, and then we find things that don’t fit in any category, what do we do?
The process of defining categories is a social construction effort. What if two people (perhaps scientists) come along and develop two slightly different categorization schemes? Whose will be adopted by the general public? Well, that depends on who publishes where, and who has what kind of reputation, and who gets their system into the public eye first.
All of these schemes have two components. First, there is the underlying physical or behavioral facts. Second, there is what humans name the categories they choose to divide these physical facts into. The latter is social construct. The former, an attempt at unbiased description of evidence (which is hard to do, since we all bring preconceptions to the process. It is hard to see things with a baby’s eye).
My point is that all categorization schemes are social constructs. Nature doesn’t give a shit what we call things. It goes blithely on being itself. We, in our attempts to model natural processes, make categories and name them. Sometimes our naming schemes become unquestioned social norms. As such, they are difficult to change, because they are so universally accepted.
The struggle to have more genders become generally accepted is not a struggle about the underlying biology. Biology stays the same no matter what humans choose to call it. The struggle is about how many categories it makes sense to divide gender into, and what we should name those categories. Of course that is a human process. Therefore, of necessity, it is a social construct.