I see that some of this has been covered, but here you go:
I suppose I'll start with length, since that's typically the first form of measurement devised for any system.
The lengths of the US customary system of measurement were taken from the older English system, and were originally defined as measurements of the human body. Specifically, they were originally established by an "average" man's measurements, and since that meant the "average" had to be established, this became the measurements of the reigning king of England, and the measurements were defined thusly:
The English word inch comes from Latin uncia meaning "one twelfth part" (in this case, one twelfth of a foot); the word ounce (one twelfth of a troy pound) has the same origin.
In some other languages, the word for "inch" is similar to or the same as the word for "thumb"...
Given the etymology of the word "inch", it would seem that the inch is a unit derived from the foot, but this was probably only so in Latin and in Roman times. In English, there are records of fairly precise definitions for the size of an inch (whereas the definitions for the size of a foot are probably anecdotal), so it seems that the foot was then defined as 12 times this length. For example, the old English ynche was defined (by King David I of Scotland in about 1150) as the width of an average man's thumb at the base of the nail...
http://en.wikipedia.org/wiki/Inch
1 foot (ft. or ') = the length of the king's foot. Foot, was the original base measurement of length in the UCS system.
1 inch (in. or ") = the widgth of the king's thumb measured at the base of the nail. This practically became the base of the system, and the foot became 12 inch measures.
1 yard (yd.) = the length from the middle of the nose to the end of the outstretched arm...of the king.
1 mile (mi.) = 5280 feet or 1760 yards. The reason for this is below:
In Roman times, the unit of long distance mille passuum (literally "a thousand paces" in Latin, with one pace being equal to two steps) was first used by the Romans and denoted a distance of 1,000 paces or 5,000 Roman feet, and is estimated to correspond to about 1,479 meters (1,617 yards). This unit is now known as the Roman mile.[38] This unit spread throughout the Roman empire, often with modifications to fit local systems of measurements.
http://en.wikipedia.org/wiki/Mile
The UCS mile was based on the same concept of roughly 5000 feet, though their yard was based on 2 feet rather than 3, which explains the difference in yards.
Of course, since these all varied every time the king was replaced, they came up with various ways to set a standard, and the standard was set not by what may be thought to be logical, but by the most reproducible means of obtaining the same measurement as the standard of the time (the then reigning king's measurements). These are now defined according to the metric system (which makes absolutely no sense if you think about it, but allows for undeviated conversion).
When you see partial inches, you typically see them in terms of halves, so 1/2", 1/4"...1/32", 1/64". This is why drill bits in the UCS system are often designated as such. It's also why you don't understand the temperature scale:
According to a letter [Daniel Gabriel Fahrenheit] wrote to his friend Herman Boerhaave,[8] his scale was built on the work of Ole Rømer, whom he had met earlier. In Rømer’s scale, the two fixed reference points are that brine also freezes at 0 degrees and water boils at 60 degrees. He observed that, on this scale, water freezes at 7.5 degrees. Fahrenheit multiplied each value by four in order to eliminate fractions and increase the granularity of the scale (resulting in 30 and 240 degrees, respectively). He then re-calibrated his scale between the freezing point of water and normal human body temperature (which he observed to be 96 degrees); he adjusted the scale so that the melting point of ice would be 32 degrees, so that 64 intervals would separate the two, allowing him to mark degree lines on his instruments by simply bisecting the interval six times (since 64 is 2 to the sixth power).
http://en.wikipedia.org/wiki/Farenheit
Does that help it make any sense?
Mass is a little more interesting. Most Americans don't know what the base system of UCS mass is...but we, who use blackpowder know it is the grain.
1 grain (gr) = the average weight of a single grain of barley and wheat
1 pound (lb - more correctly lbm - to identify it as pound mass instead of pound force) = 7000 grains
Now it can get a little confusing. Remember that little excerpt fromt he length citation that mentioned ounce is derived from the Latin word
uncia meaning 1/12? It does mean 1/12 of a pound - in the troy system, which is now only used in gemology.
In UCS,
1 ounce (oz) = 1/16 pound
I cannot find a specific reference (or remember anything specific) as to the origin of the UCS ounce, but suspect it is directly related to our love of fractions in base 2 (1/16 is 1 pound halved 4 times).
You complain about not understanding why we continue to use our archaic system of measurement - and I agree with you, but now you can see that it is based on direct relationships of everyday objects that the average person could observe. The SI (or metric) system is is also based on a directly observable relationship - and it's superiority over the UCS system lies in the object that it is based on - water. Most of it is defined according to water's attributes - weight, mass, volume, size, and temperature. Using such a universally available object for a base made it superior to all other systems of measurement and combining it with a base 10 numerical structure makes it convenient to use.
