It could be because of the Bayer (color filter) array, although that depends on the camera manufacturer making a particular set of decisions.
Adjacent pixels have filters in front of them that make each pixel responsive to one set of wavelengths; a full-color image is produced using algorithms (called "demosaicing") that propagate the color values from the pixels that capture that color to neighboring pixels (not always in linear ways; there might be edge-detection or other clever algorithms involved).
If you bin pixels at the stage where they're read out from the sensor, before the demosaicing algorithm runs, then the demosaicing won't work properly, and needs to be bypassed. In the simplest case (an RGBG array and 2x2 binning, or any multiple of 2), the binning perfectly erases the color information because every bin contains all three colors, in the same proportion as every other bin (1R : 2G : 1B). In less-simple cases there could be some residual color-spatial information left after binning, but it would require a different algorithm to resolve, and it would be of poor resolution anyway, and not really worth bothering with.
But couldn't you do the pixel binning after the demosaicing? Yes, you could. And if the purpose of binning is to reduce the bandwidth going to the PC, it seems that you should. So why not do that? I've tried to think of a reason, and I can only come up with one sensible one: the manufacturer decided not to implement demosaicing in hardware, to save money — it's done on the PC instead. If that was the case, demosaicing before binning wouldn't be an option, and you'd be stuck with monochrome.