Why there is no brown or grey in the CIE XY color space?
The xy chromaticity graph isn't a color space; it's a two dimensional projection of a color space designed to separate hue and saturation from luminosity. To represent gray and brown you need this third dimension since grey is basically dark white and brown is dark orange. A 3 dimensional color space like xyY where Y is a third dimension representing luminosity has no trouble with grey and brown. In this case gray values would extent down from the white point and browns would extend below the orange.