For me, being non-binary is a very private thing. I don't want every social occasion to require educating people about what it means to be non-binary, and I want unconditional acceptance in female spaces, so I present as a binary female. My concern is that the females who I need social connection with will see me as "different" if I introduce this wrinkle.
So I save the fact that I'm non-binary until I know they will not see me as some sort of Other.
I like the term "non-binary" because it is inclusive. It doesn't set out parameters for what we have to be, only parameters for what we're not. The old word, androgyne, had such a narrow definition, that I was forever trying to figure out whether I fit into it.
But as much as we hate the idea, the vast, vast, majority of the population is happy and comfortable identifying with one of the two binary genders, and most are untroubled by the reality that everyone expresses and lives their gender in a slightly different way. So a woman who drives a big rig, for example, doesn't see herself as "between the genders" just because she engages in activity that's uncommon for a woman.
Non-binary people love to have this fantasy that most binary men and women secretly think of themselves as between the genders, but I haven't seen any evidence that this is actually true. Others have this fantasy that most men and women are dissatisfied with their gender and would be "gender-freed" if society were less constraining, but I don't see any evidence of this either.