How I understand it, gender ideology is a model. It assumes a spectrum of behavior between men and women and your position on this spectrum means if you are a man, woman or non-binary. It does not define what it means to be a man or a woman except some vague behavioral traits about what it means to be a man or a woman. Matt proved this this in his documentary where professors and doctors could not define what a woman is. The model is not consistent, a man will change his personality and in time will not be as "tough" as he was in his 20s - early 30s, according to gender ideology then he can no longer be a man at one point. To make things even crazier, being sick as a man is very un-manly so it means that a bad cold can make you a woman. It does not reflect reality, under this model butch lesbians and feminine gays should actually be trans but they are very happy being who they are. This is why no one on the left can provide a definition.
It hurts children. Children need structure and purpose, not confusion about what they are. How many girls get sucked in to believing they are boys because they do not fit in? This is not leftist manipulation but applied gender ideology. They do not fit in the category of girls hence they are something else.

What is the advantage of this model? What does it offer? If at this point in time you are non-binary, does that give you any advantage, does it solve any issues? 

From 90s to 5 mins ago the used model was one where your behavior did not change what you were. You could be a girl that liked football and not be less of a girl then one that liked dolls. This model offered a lot of freedom.

So why do we need an incredibly bad model over a model that worked much better?

Only reason is leftism. Leftists use and push for it. So you can't in separate the ideology from leftists using it to feed in to narcissism, authoritarianism, victimhood as a virtue, alienating kids from their parents and hurting the nuclear family and even national identity.

Is a bad, inconsistent, illogical model that causes harm to children and adults and the only reason it exists in our life is to be a tool for marxists.