I have never really identified with the term "non-binary". Even though by definition I am a non-binary person, I avoid using it and don't like other people using it to describe me (when I describe my gender, I always say I'm "not a man" rather than saying that I'm non-binary).
To me, the term "non-binary" feels wrong. It's a term that is defined by the gender binary, and one that is rooted in the assumption that the gender binary is immutable. To describe somebody as being "non-binary" is to describe them relative to a model of gender that we should be working to dismantle.
I'm not saying that non-binary people are invalid (hell, I am one) but that the term is problematic to me. Anybody is free to identify with whatever term they want but I don't like "non-binary".