Twelve is 2 x 2 x 3, and it has six divisors, 1, 2, 3, 4, 6 and 12, which is more than any smaller number has. That single property explains most of where twelve occurs, and it explains it better than any symbolic account does.
A quantity divisible by two, three, four and six can be halved, thirded and quartered without fractions, which is why twelve was the base of so many trade and measurement systems: twelve inches to the foot, twelve pence to the shilling, twelve items to the dozen and a dozen dozen to the gross, twelve ounces in the Roman pound. The persistence of these units long after decimal alternatives existed is a practical judgement rather than a superstition.
The calendar supplies the other half. Twelve lunations come to about 354 days against a solar year of 365, a mismatch of eleven days that every lunisolar calendar has to absorb by intercalation. Twelve is therefore not an exact fit, it is the nearest whole number, and the awkwardness of the remainder is the engine behind a great deal of ancient astronomy.
The zodiac follows from the same arithmetic. Babylonian astronomers divided the ecliptic into twelve equal signs of thirty degrees by the fifth century BCE, replacing an earlier and untidier set of constellations, and 360 divides into twelve exactly. The signs are a mathematical division of the circle onto which constellation names were mapped, not a description of what is actually up there, which is why the constellations they are named for are of very unequal size.
Chinese reckoning uses twelve earthly branches, paired with the twelve-year cycle of Jupiter's orbit, which takes 11.86 years, close enough to be usable and wrong enough to require correction.