Taylor argues that our identity is in large part our sense of where we fall in relation to matters of human significance. It is about where we locate ourselves in moral/evaluative space. Here's how he puts it in The Ethics of Authenticity;
"When we understand what it is to define ourselves ... we see that we have to take as background some sense of what is significant. Defining myself means finding what is significant in my difference from others. I may be the only person with exactly 3,732 hairs on my head, or be exactly the same height as some tree on the Siberian plain, but so what? If I begin to say that I define myself by my ability to articulate important truths, or play the Hammerklavier like no one else, or revive the tradition of my ancestors, then we are in the domain of recognizable self-definitions.
The difference is plain. We understand right way that the latter properties have human significance, or can easily be seen by people to have this, whereas the former do not..." [Emphasis added]1
So then, it is understandable that peoples' identities include things like being good at football, or being a conservative, or knowing a lot about the Bible, or being born in a city famous for its musical culture, or whatever. These relate to things of human significance. But how about gender identities? Do these relate to things of human significance?
Being a woman or a man is clearly not just a mere physical fact that one should get over. It's not comparable to, say, just having a strong big toe, or having a mole on your back. These are trivial things. But being a man or being a woman is hugely relevant to important human endeavours, namely the whole package of mating; the attraction, the sex, and (at some point) childbirth and child-rearing. It is humanly important that there are men and there are women – that there isn't just one sort of human. The kind of beings that we are makes this important.
By applying Taylor's insight we can see that gender identities exist (at least partly) because of the significance that is found in biological sex. So as child grows up, he or she learns that social space consists of men and women. As the child's self-awareness grows he/she gradually become more conscious of which part of social space he/she is in. The child learns, “I am a girl” or “I am a boy”. More than that, he/she learns that it is significant which he/she is. That it's not a throw-away fact about them. It is a fundamental part of their identity – of who they are.
Gender identities will be around as long as biological sex carries human significance. And you should be careful about forecasting the demise of that any time soon. We can rightfully challenge the kinds of gender identities our culture has developed but it's unlikely that we can do without them.
1Taylor, Charles. The Ethics of Authenticity. Harvard, 1991, pg35-36.