This makes zero sense though. (Not your explanation, specifically, but the whole idea.)
Firstly, humans can't change sex. A male person who identifies as female is still in fact male and vice versa. It makes no more sense than saying you identify as a unicorn. Like, yeah, OK, but you're not one.
Secondly, as nonsensical as I find it (because humans can't change sex), a male person who identifies as female is still identifying as something understood and defined. They might not actually be female but at least we understand what female means and what it is they think they are identifying as, even if we don't agree that they can actually be female in any meaningful way.
Non binary is just...nothing. They're identifying as not being something (that they in fact are). But the identity itself doesn't exist. It's the absence something. It's like saying you identify as nothing, or an existential void.
The only way to actually explain it is that non binary identifying people don't identify with the regressive stereotypes that society chooses to attach to men and women.
OK, fine.
But loads of other people don't identify with those stereotypes, without pretending they're neither male nor female. Most people don't conform to them in fact. In truth, the people who uphold and entrench those stereotypes the most are the very same people who think they're challenging traditional received wisdom about gender by identifying as trans or non binary.
By saying that your gender is non binary, you're saying that there is a binary that you identify out of. You're labelling everyone else as people who conform to binary gender stereotypes (whether they in fact do or not) purely so that you can label yourself as someone who doesn't conform to them.
It's actually quite insulting when you think about it. "I'm non binary" essentially means, "I think everyone else is a boring conformist and I am different and special."
And people who think they are different and special are frequently an absolute pain in the arse in situations where they have to rub along with other people, such as school or the workplace.
The concept of non binary is also nonsensical from both a literacy and numeracy point of view. Binary means there are two options. If you create a third option and call it non binary I'm going to go right ahead and assume that you don't know what binary means.