Why do beekeepers need to wear protective clothing?

Beekeepers wear protective clothing so they will not be stung. One or two stings is annoying and painful, but large numbers of stings can be fatal. When you are working around entire hives of bees, large numbers of stings is what can happen if something goes wrong.

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Just to add to the previous answer, I teach beekeeping, and I have heard the odd student say something like 'Oh, my bees are so calm I don't really need my bee-suit.' My response is that one must always wear protective clothing. You can go to the bees a number of times and they are perfectly calm. The next time you go to them and open the hive they would fly out on the attack, and you won't know why. Bees are wild animals and cannot be tamed, and you just can't take the risk.