Ahhhh I think it's more a case of you not knowing what 'gender' is, actually. Gender refers to a social construct - a stereotype - that society assigns based on its perception of a person's physical sex. So a male (biological) is expected to act masculine (sociological.)

Basically the definition of male is pretty constant, since it's physical, and doesn't really change from culture to culture - chances are if you've got a dick and a couple of balls, or if you've at least got the genetics for it (intersex people or hermaphrodites being a gray area) then you are male, no matter where you live. But what makes you a man does vary from culture to culture, maybe more widely than you'd expect, and always has depending on time and place.

So when people say they're agendered, they saying they don't feel like the identify with 'masculine' or 'feminine' as defined by their society. Alternate genders are an attempt to identify as something other than the default two - the binary people mention. And non-binary can refer to not feeling like they fall strictly into either 'man' or 'woman' categories, to whatever degree.

The best way I've come up with to think about gender stuff is: how would you feel if someone mistook you for the opposite gender, and expected you to act a certain way because of their perception of you as that gender? In other words, do you identify with your gender to the degree that you'd feel defensive or threatened if someone got your gender wrong? Because that's essentially how these people seem to feel. They've bought into the idea of gender itself, but the gender that society recognizes them as feels wrong to them, the same way that being treated like the opposite gender might feel wrong to you.

I dunno. People are complicated. It's easy to dismiss stuff as just stupid or whatever but that's kind of doing yourself a disservice.

Also holy shit this was a long rambling response to your comment. Sorry.