History of Wool
Sheep hair was more like deer hair is today, short and thick, not long and fine and curly. Like goat hair.
Then around 10,000 BC people in West Asia began to domesticate sheep (tame them) and take care of them, so there would always be plenty of meat around. At this point they began to use the milk from the sheep also, either drinking it fresh or making it into cheese. When they had killed a sheep, of course they would also make the skin into leather, and maybe leave the hair on to make it warmer, like a fur coat. But still there was no wool as we know it today.
Man shearing a sheep, about 1550 AD (Brueghel)
Sometime not too much later people also began to make clothes, instead of just wearing furs. Since they had sheepskins around, one of the fibers they used was sheep hair. They noticed that although none of the sheep hair was really any good for spinning, because it was too thick and brittle, some of the hair from the stomach, the underside of the sheep, was better than the rest. And people began breeding the sheep that had the most good hair together, trying to get some hair you could spin. It took thousands of years, many many generations of sheep, but by about 5000 BC, people could begin to spin wool.
Sheep being sheared for their wool on the Isle of Skye, Scotland
Wool has a lot of advantages over vegetable fibers. It is easier to prepare it for spinning: you just cut it off the sheep and comb it out. It is easier to spin than cotton or flax, and quicker. It is warmer (that's why sweaters are made of wool, and sometimes socks, and blankets) (though this is also a disadvantage in very warm climates like Egypt). The lanolin on the wool makes it shed water, so it is a good fiber to wear if you will be out in the rain (as shepherds often are). And you can dye it more easily than flax, so you can have clothes in pretty colors and patterns.
For more about wool, check out these books from Amazon or from your library:
Warm As Wool, Cool As Cotton, by Carter Houck (1986). For kids - includes the history of these fibers.
World Textiles: A Concise History, by Mary Schoeser (2003). For adults.
Women's Work: The First 20,000 Years : Women, Cloth, and Society in Early Times, by Elizabeth Wayland Barber (1995). Not for kids, but an interested high schooler could read it. Fascinating ideas about the way people made cloth in ancient times, and why it was that way.