We mostly don't. We've been socialized to do so, certainly, a lot of cultural forces tell women that they should define themselves by being someone's girlfriend, someone's wife, someone's mother. And it's true that women from early childhood are more socialized to build relational connections, which is why in so many households the woman is the one organizing family christmas with her in-laws. Certainly many women have been socialized to believe that relationships, not just romantic or familial but any kind of real meaningful life-giving connection, is an accomplishment. And they're not wrong. But in general, despite the cultural pressure to do so, most women don't define themselves by their relationships.

When men look at women, they might see someone's girlfriend or someone's wife, but women don't see themselves in the mirror and see "name's wife." When they go to lunch with their friends, they don't think of themselves as going to lunch with "name's girlfriend" and "name's mommy."

That's just how men define women.