Non-binary is a broad spectrum of identity. What you're suggesting only works for identities like genderfluid or demi-gender people.

I'm agender, which exists outside of the male-female binary (in which you are either one or the other). Agender and it's derivatives, like gendervoid, are completely gender neutral. I only use they/them because it's really difficult for the average person to not use a pronoun when referring to me, I very much prefer people using my name in place of one.