The categories that encompass "man" or "woman" or whatever are socially constructed. The outlines of those categories especially are so far from being absolutes of nature or physical constants.
But people still have an innate sense of themselves and their own identity. So even though the rules are made up and the points don't matter, people can still know which box they go in based on that sense.
For some people, they're just comfortable in the box everyone right they'd go in and never think about it. Stone people don't care which box they're in and so never bother to think about it. There's all our cis folks. Stone people don't really care which box they're in, but they do still think about it and decide they go outside any of them. Some people think they go in one box sometimes and either box at other times. There's the nonbinary folks. And then there's people who can tell they fit in a box, but everyone seemed to think they're actually in the other one until they mistake was pointed out.
The boxes themselves are totally made up, but they still exist. And since they exist, people can still tell which ones they go to. The fact that the boxes are fake doesn't make them not "real", it just makes enforcing them and telling people you know what big they should be on better than they do stupid.