@hurokun that’s not quite right either. Sex is bimodal, meaning *usually* you’re in one of two positions but not always. You can have extra chromosomes, or be missing one, so not everyone is XX or XY. Then, it’s not even merely a Y chromosome that does it, but a couple of genes on the chromosome that can either be missing or transcribed to an X. Going more phenotypically, you can lack receptors to certain hormones, or have unusually high or low levels during development and later life. And not to mention deliberate interventions in later life, such as taking hormones, which also have an effect on the brain — we know that cis people get real miserable given cross-sex hormones, while in trans folks that misery is alleviated.
All of this is to say that physical sex is really a cluster of variables, some of which binary, some having several possibilities and some on a continuum. These *usually* all line up neatly into the bimodal distribution, but given that we usually paper over these details, sex is socially constructed too.