Jacob,
You want to use a 1/120th shutter at 60fps because that gives you a 180 degree shutter. This is how a film camera works to give the most fluid motion possible. That means that there is an equal amount of time between the frame being exposed and the time in between frames. You basically double whatever your fps is and that give you your shutter speed.
Now this does not mean that you couldn’t have a 90 degree or 45 degree shutter. Like Rob was saying, that would give you a different look; in this case choppy because your shutter is closed for a longer period of time than it is open.
