Have you ever tried to whiten wool cloth with household bleach? If you have, then you know the result is a yellow, dissolving mess. Why is it okay to bleach cotton cloth, but not wool?
It all boils down to simple chemistry. Household liquid bleach is a basic chemical, with a fairly high pH of about 10. Bleach whitens clothes by releasing oxygen that combines with chemicals in dye, making them colorless. The higher the pH of bleach, the greater the amount of oxygen that's released, and the whiter your clothes become.
Like bleach, cotton fiber is also on the basic side of the pH scale, and cotton usually bleaches well, but wool is acidic. When you combine acidic wool with basic household bleach, you get a chemical reaction called a neutralization reaction, and the result is that the bleach dissolves the wool fibers into a goopy mess!
That's why you can't bleach sheep at home, but commercially, wool is whitened by soaking it in acid before and after it's bleached. The acid helps neutralize the pH and prevent the bleach from dissolving the acidic wool.
You can try an experiment to see what bleach does to wool fiber-without damaging your wool clothes. First, get a small clump of hair from a barber or salon. Like wool, human hair is acidic, so it reacts with bleach in a similar way. Put the hair in a small jar, then add bleach. Soon, you'll see foam on top, and little bubbles on the hair. The hair will start to dissolve, but at least it isn't your favorite wool sweater!