The spoiler is there to press the wiper blade on to the windscreen when you are driving (air flow over the spoiler). You tend to only get a spoiler on the drivers side as this is more important. I assume they don't put one on the passenger side inorder to save money (and charge you less).

The aerodynamics of your car could cause the passenger wiper to lift from the screen at high speeds. The spoiler will prevent this (in theory). The drivers side arm pivots from a more central point, and is not subject to as much turbulence.