There comes a time in life when you need to build a bridge, and then get over it. I think the "traditional" perspective of binary gender is one of these examples where a bridge is needed for much for our population.
If you think about it, it's quite astonishing to think that every single human being in this world fits in one of two categories, male or female. That's 7,000,000,000 people, woah. There's nothing else that uses binary differentiation for humans: eye colour, hair colour, height, weight… just to name a few. Even seemingly binary things such as being left- or right-handed isn't really binary. Ambidextrous people make up around 1% of the population too.
So why are we so obsessed with categorising our children as being male or female; boy or girl? Does our physical appearance, that is — genitalia, really define who we identify as? I think one great parallel is with an individual's cultural/racial identification in relation to physical appearance. Imagine this scenario:
If a child was born from two Chinese parents, but raised entirely in Australia by your typical "Australian family" (say the child was adopted)…. when that child grows up, they wouldn't identify as a Chinese person at all… yet, they would definitely look the part.
What "nationality" would you class yourself as if you were in that situation? Is it because of your Chinese appearance that makes you who you are? Or would you be identifying yourself based on who you think you really are culturally… an Australian? I would think the latter.
It's much the same story with gender, in my opinion. Traditionally, we see individuals by what body parts they were born with, without actually understanding who they are or what gender, if any, they identify as. But I think if people actually took the time to contemplate the great varieties of humanity, there is no such thing as binary gender… it's only something we as humans, have enforced on one another.