Gender roles were both ignored and highlighted in my house... my mother was the type that did sit-ins in high school in the 60's to wear pants to school because she hates dresses, and she always made a big deal that girls can do anything boys can do, but whether I was doing "boy" or "girl" stuff was never highlighted. My father wanted me to be a super-smart science genius and it didn't really matter what gender I was: I was the firstborn and thus I would be wonderful at all things.
So for years and years I'd just read whatever and play with whatever and do whatever, and at school I'd spend more time with boys and my family just figured that's because I was a "nerdy" sort. But I'd still identify with female characters and I always wrote about female main characters in my stories. Why? Because I was a girl in body. No other reason. It was a very literal thing. I'd dress depending on how I felt... sometimes like a boy, sometimes like a girl. I guess being female-bodied people accepted "boy clothing" as okay for a girl.
When I hit puberty I finally went "oh hey I'm supposed to be a girl!!" and started perming/dyeing my hair, pierced my ears, joined a female-only youth group. But at the same time I wanted to cut my hair super-short. I've spent a
lot of time trying to figure out how I'm "supposed" to be. I talk a lot about presentation here because really to me that's the only way I can pin down gender in my own life--by what other people say is male or female. Probably if I was going to make up a species with two genders, everything I like would be my gender, and everything I don't would be the "other" gender. I don't even know what I'd call them though. I don't think I'd make there be two. Maybe four? Five?

Really though... and I'm a writer so that's probably why I see it this way... realizing that I identify with characters based less on gender than on personality made me go "I'm not really female in my mind." And I know, I know, men can identify with female characters and vice versa but that's not what I mean... I mean something I don't quite have words for, and it goes back to when I started reading (which was when I was 3), wherein I could totally identify with both little girls and little boys... and even little non-gendered alien children... because it didn't feel "weird" or "wrong" to imagine myself as one or the other. Or maybe it felt equally "weird"... leaning one way or another.
My favorite books have also often included some aspect of changing sexes, or body swapping, or sharing memories of other sexes (I'm thinking heavily here of the Atreides children from Dune Messiah and Children of Dune...)