I'm only reporting what I have heard from the non-binary people I know - that they wish to be seen as a whole person who has both stereotypically male and female characteristics - which of course we all have. They don't see themselves at fitting into a binary which is linked to gender roles and acceptable gender expression, although I'm sure that differs from individual person to person. Some may feel like both genders, some may feel like they are neither, and there may yet be other options I'm not aware of.

I don't think they are saying that gender doesn't exist or that it isn't acceptable for some people - they are saying that it doesn't work for them. I see myself very much as a woman, and happy to be one - even if I don't always appreciate some of the societal aspects that go along with that. I don't think the concept of gender is going anywhere - but hopefully the concept of what is acceptable for and what is expected of people based on their gender will.