The reason a clock uses 12 hours is actually simple: use a compass/forked stick in the sand to make a circle. then, naturally one would place one leg of the compass at some point on the circle, and draw a second circle. then, one would naturally place the leg on one of the intersections just made, and draw a third one. 3 more times, and you have gone all around and drawn a pattern of 1 circle in the middle (the 7th) and 6 circles around.
This means that, division in 6/12 is the easiest, and also most accurate way of dividing a circle in the past. Dividing a circle in 5/10 parts is really hard to do accurate with only the 'euclidian tools'(pencil, ruler, and a pair of compasses).
Note also that a number system based 60 is easy to make calculations with. Imagine a dollar having 60 cents, makes it much easier to share this dollar with 2,3,4,5,6 people. Also note that you can count 60 on your fingers, when counting 12 digits on your one hand, and 5 fingers on the other hand (5x12=60). Doing this, you even do not need one thumb, so you can hold your merchandise while counting :)
Since your question is about accuracy, i need to add that while we think of an hour now as a fixed unit, before the invention of the clock, hours were 'variable' in the sense that a day is shorter in the winter, so while there was a division in 12 parts, the parts were not always equal.