So, to answer the original questions. What does it mean to be non-binary? Your sense of self simply doesn’t conform to the ideas of man or woman, and that may be because our brains don’t conform to them either.
How can you be something other than a man or woman? There are lots of people who do not fall onto those parts of the continuum of biological sex. It’s actually pretty normal not to be a typical man or woman.
See the conflation? Sense of self is gender identity; what you are is gender. These are two different things.
I think the root question we have to ask and answer is whether the difference between male and female is qualitative or merely quantitative -- not our perception of them, but in what they are, in and of themselves.
That is, if you believe they are anything, in and of themselves.