If you want to see the foundations of our society, ask and investigate what create social status. Even at preschool, kids usually arranging themselves into group with a hierarchy. Usually those groups are separated on gender, through at the youngest age group they tend to be a bit mixed and by the time kids hit puberty its almost fully sorted into groups of single-gender. Age 5 to 10 should provide a bit of insight into this process.

What signals is encoded in our society that make one girl to get higher social status among other girls. Similar, what signals are encoded to give one boy higher social status among other boys. In that difference between the two strategies for social status, what incentives has parents if they want their child to have high social status among other children.

From that point we can look at what puberty does to the incentives to maximize social status among one own gender, and the relation to dating. Add a few additional years and they have to pick career paths with accumulates all those incentives into a point where gender segregation really start to pick up speed.