First off, gender and sexuality have nothing to do with one another. Sexuality is who you would be attracted to, and gender is who you ARE. Then you also have gender expression, which is how one chooses to express their gender, this may or may not be in the traditional way. For example, I may identify as female, but I express my female-ness through strength. Note how I didn’t say ‘femininity’. Femininity and masculinity are cultural concepts. What is feminine in one culture would not be feminine in another.
Anyway, second: Gender is a spectrum. A simplified explanation of this can be found in the image above. This means that gender isn’t just black or white, male or female. There are varying degrees of ‘male’or ‘female’. And where you fall on this spectrum is your binary gender.
Some people however (including myself) do not fall anywhere on this spectrum. We feel non-binary. There isn’t really a way to explain how this feels, but just as someone may feel and identify with male, or female, I identify as non-binary. It’s what makes sense to me, and makes me feel at ease.
Non-binary is an umbrella term, with various other identities, such as third gender (a gender other than male or female).
Ultimately, your gender is your own, and it’s such a complex thing that labels will not always fit perfectly. It’s like wearing a shirt which is a size or two too big for you. It fits, you can go around with it, but you know its too loose. Still, a shirt which is too big is way better than a shirt which is way too small for you and you just feel constrained.