I believe that gender is a product of socialization, and therefore you cannot be of a gender that isn't recognized by society.
I get trans women/men, because they essentially are assigned to one out of the two recognized genders (male/female) but identify themselves and want to be socially recognized as the opposite.
Non-binary genders aren't really a part of society. There are no gender roles for a "demi-boy" or a "agender" person. It makes no sense that someone wants to be recognized in one of these categories because these categories essentially don't exist to society.
How is it not just a term for saying that you act outside the gender norms that were assigned to you? How can one identify with these genders if there is no such thing as a social product? And if it is indeed just about behavior/ how is this not offensive towards trans people? How is this not trivializing gender identity??
EDIT: about the "ploy for attention" thing, I'm truly sorry if I offended anyone. As /u/_mach pointed out, this is likely confirmation bias of my part because most of the exposure I've had to non-binary people was on the crazy realms of the internet/tumblr. The fact that some people are doing this for attention shouldn't mean that everyone is.
EDIT2: I think I genuinely have a better understanding about this now. I don't doubt there people exist or that their experiences are valid. I guess I'm still having some trouble with concepts, as I explained in a lot of my comments in this thread. It's not as much as I can't believe a non-binary experience is real/valid, but that I can't really understand how it's more than just a gender performance/expression and actually constitutes a new identity. Most of the comments were super helpful though at broadening my understanding of the topic. Special thanks to all the non-binary and trans people who chimed in on this.