Can't exactly tell you why 1/48 rather than 1/47 or 1/49 other than ease of calculation but, scale modeling grew up over a period of time from small beginnings. Different manufacturers all over the world began to produce injection molded plastic kits and there was no real reason for them to coordinate their efforts, so they produced models at scales that they each felt appropriate.
Thus, one manufacturer might be producing a range of aircraft at 1/76th scale while another might bring out a similar range but at 1/72nd scale. In the early days of the hobby standards were much lower than today and the exact scale did not seem so important. Some models – particularly those of cars and fictional subjects (such as science fiction craft and monsters) did not even quote a scale.
Over time there has been a tendency for scales to become standardized as the market has become more globalised and dominated by a few large manufacturers. Up to 2004, military vehicle (MV) modelers had two main choices of scale, 1/72nd and 1/35th. At the end of that year, Tamiya announced the introduction of a brand new scale that at 1/48th was right in the middle of the two and tried to capture the advantages of each existing scale. The 1/48th scale had been popular with aircraft modelers for a long time, but this was effectively a new scale for MV modelers.
Sometimes a part of a model may be deliberately out of scale to make the model appear more realistic, or for practical reasons, for example:
On a sailing ship, the thickness of the sails may only be a few millimeters. A typical scale for a sailing ship is 1/144th and at this scale the thickness of the sail should only be a fraction of a millimeter. Even if a model sail this thin could be produced, it would be very fragile.
An armored vehicle is usually adorned with hundreds of bolts and rivets. At 1/35th scale, which is probably the most popular armor scale, every bolt and rivet can be faithfully reproduced although they will be very tiny. However, on a 1/72nd scale tank, details such as bolts at the correct scale may be too small to be seen by the naked eye and certainly too small to produce. To be totally accurate, all of this detail should be left off because it could not be seen. However, if this was done, the model would look very simple and 'toy like'. Thus most modelers will include these details even if they are 'over scale'. Sometimes there is a conflict between 'scale accuracy' and 'apparent realism' and most modelers in these cases will choose realism.
Some modelers like the challenge of a really big model with hundreds of parts, where every detail can be faithfully reproduced. These models have the disadvantage of being expensive, difficult to store and take a long time to build. Other modelers prefer small scales and this may be for practical reasons such as cost, ease of building, display and storage etc. Another reason for choosing very small scales is that some modelers like the challenge of reproducing every detail in a very small model. Building in small scale is not necessarily an easy option and some of the better small scale models have the same number of parts as their larger scale big brothers.
Another practical reason for different scales is the size of the original that the models are based on. Warships are often built in scales of 1/350th or 1/700th because warships are generally very, very, big. If one tried to make a 1/35th scale model of a World War II battleship it would probably not fit into most modelers' houses. This is the reason why the larger the size of the original the small the scale that will tend to be commonly used.
Ship modelers tend to work at scales of around 1/350th. Aircraft modelers work at 1/76th or 1/48th depending on the type of aircraft (1/48 is the traditional scale for Admiralty Board style models and Shipyard builders) models. Larger aircraft models fall into the 1/32 scale (1:32 was once so common a scale for toy trains, autos, and soldiers that it was known as "standard size" in the industry. Also known as the 3/8th scale since 3/8th of an inch equals 1 foot. It's also the 54mm scale used in miniature soldiers in wargaming) Armor modelers tend to use 1/35th scale (1/35 as a military modeling scale lie in early motorized plastic tank kits. To accommodate electric motors and gearboxes, these models needed to be made in a larger scale. There were many companies making such tanks, but it was Tamiya's example that made 1/35 a de facto standard. This size had been chosen simply because it would accommodate a couple of B-type batteries). Car modelers tend to use 1/12th scale.
The model railroading hobby used letters to describe scale. Widespread standardization among the various rail-scales allowed for use of a simple letter code. Originally, the code referred more to gauge - the distance between rails on a given piece of track - than to scale. Thus O gauge meant model trains that used track whose outside rails were 1 1/4 inch apart. It's no coincidence, then, that HO would mean "half-O", for purposes of gauge. As interest in scale accuracy grew among toy train fans, the letters came to represent a scale moreso than a track width. Thus, O scale is 1/48 - in other words, a train that uses track 1 1/4 inches apart would be 1/48 scale. Scale and track width soon were distinguished. The plain letter denotes a scale and its gauge, while other track gauges within that scale get special attention. For instance, "HON3" means HO scale, using a narrow gauge track. This track is 3 scale feet wide, as opposed to the normal four foot- eight inches of standard railroad gauge. The N tells us that this is narrow gauge. HON30 is different, meaning narrow gauge of 30 inches. By the way, HON30 is the same track gauge as the smaller N scale! As trains went from toy to scale model, thus the letter code changed from gauge to scale.