Why does LVDS (or any differential signaling for that matter) use a common mode voltage of 1.2V instead of 0V?
Because, then the signal would have to be negative also. The trick is to use a positive single power supply. Now the differential signal is centered arround 1.2V and the applied differential signal is +/-175mV. 

Using a 0v common mode, the signal would be +/-175mV meaning that you need dual power supply - negative and positive at both sides, which is more expensive.