Gender Binary: In gender theory, there's a differentiation between biological sex and socially assigned gender identity. Although in strict biological germs, there's a relatively large intersex community that throws the whole biological sex binary into some complication. That's not usually what's referred to here, but there's info out there if you're interested in it.
When people speak about gender binary, it's predicated on the idea that men and women have discrete characteristics or traits that are natural to their gender. Biological determinism posits that the gender attributes are tied into sex - which is which I suspect there's some confusion when the idea of a binary being opened up causes confusion. Examples of a biological determinist position include the idea that women are naturally better suited to the raising of children (note, raising, not bearing), housework, like pink and are poorly suited to leadership roles. This collection of ideas and others like it broadly are taken to be immutable, unchangeable and essentially true. It's almost positing an ontology of femininity that people participate in by virtue of having a vagina. Social constructivist theory, however, takes issue with this. It claims that men are capable of identifying with traditionally female / feminine 'traits' and vice versa. What it responds to is the conflation of traits at all with biological sets - it's essentially saying that you aren't a 'male' or 'female' by virtue of what you do, how you act or how you express yourself.
Men that like to bake and watch sex and the city don't magically lose their balls and women that like power-tools and gaming don't suddenly sprout knobbage. The argument for why people adhere to gender roles is assigned (broadly) to tradition, social pressures and cultural expectations, consolidated into what is sometimes referred to as a 'cultural script' - I.e; the roles / lines we're meant to say in certain situations. It's subconscious, largely socially defined and not absolutely and always true - but if you look around, you find tell-tale signs of it around and about quite a lot. The main point of criticism that SCs make of determinists is that there's a conflation of what happens to be incidentally true to being absolutely / universally / 'naturally' true. A case study can be found in the study of boys => blue, girls => pink trope of western society. Until 50 years ago, it was the other way round. Yet today, there are instances of evolutionary psychologists attempting to find (pseudo)scientific rationale for women liking pink because berries were pink-coloured in the distant, murky past of our species.
So, the aim of a social constructivist theory of gender is often emancipatory. People should be free to do as they will and express or define their gender identity as they see fit. As such, the binary of how we perceived gender in relation to particular traits / acts is broken down. If I want to make a cake - and I frequently do - then I can do so without feeling like I'm doing something violating cultural norms.
IMO, it's all a knock-on-effect of people operating in a post-modernist epistemological context. At least, in the west.
However, for the purposes of the poll I was assuming that the author was referring to male / female as markers for biological sex. So the in-depth discussion about the gender binary isn't strictly relevant.
Things get more complicated when you integrate class or race or consider transgendered / cisgendered as well. But then you're getting into more complicated and nuanced things-and-stuff. My favourite quote from a random academic whose name I've forgotten is 'Strictly and historically speaking, woman doesn't exist'. Yay for deconstruction taken to its logical conclusion!