Why would one choose 12 V from 24 V, from a safety standpoint? I have seen many people saying on this site and many other 3D printing websites that 24 V systems are safer, compared to 12 V systems. By safer, I am talking in terms of fires or other electrical and component failures. 

Why would a 24 V system cause less danger? I would think that 12 V would be safer because it is very common (automotive) and many parts have been around for a while that use it. Although there are an increasingly amount of boards that support 24 V, many don't or need fuses or other parts that do support 24 V. 

Also, many parts that I have used are rated for 12 - 24 V. A 12 V power supply can go a bit over fairly comfortably. A 24 V power supply can't without partially going over the rating.

If I had to build a printer designed with safety as a main priority, what voltage would be best?
The most important "safety" advantage when using 24V (compared to 12V) is that to get the same power, you only need half the current. A 192W heated bed would need 16A at 12V, but only 8A at 24V.

Since one of the most common safety issues is underrated screw terminals being used for the heated bed (just search for "3d printer fire"; you'll find quite a few pictures of charred plastic around screw terminals). For example, the screw terminals on RAMPs board are only rated for up to 12A. That would be okay at 24V, but well over the limit at 12V.

Since the wire gauge is dependent on current, you can also use somewhat thinner wires with a 24V system (or equivalently: wires that would melt in a 12V setup won't in a 24V setup). The power dissipated in a wire scales quadratically with current, so the same wire being used in a 24V setup would only waste a quarter of the heat of that wire in a 12V setup. There is also less strain on switching devices (such as MOSFETs or relays). The same applies here: power loss is quadratic with current.