Here is one of my kids sporting a giant nerf bow and a sparkly dress.

3 of the kids wear this size.  Boy sex or girl sex?  Boy gender or girl gender?
(obviously I gave away the answer to the kid's biological sex on the previous post)

Sparkly McFabulous, Bounty Hunter, here feels just slightly more girl-gendered than boy, given only those two choices, but presents as boy most of the time.  At our home, and sometimes even out in the world with us, Sparkly McFabulous enjoys presenting this way.   We went two the doctor and Sonic today, and someone was very happy about being complimented about looking pretty in the dress.  We made things easier by not using pronouns while we were out.  I take Sparkly to whatever restroom works for Sparkly.  I have a friend whose biological daughter presents as male at a young age, flatout refusing to wear "girls'" clothes.  That's a little easier to get past the gender police.

Why is the system binary?

I would choose neither, honestly, which is why I say I am FTM.  I am not really male.  I am not really female.  I am just me, and I would prefer a more male body.