The simple answer is because it makes them feel better. Several answerers have cited reasons and they're right Amy, but  there are a lot of reasons in addition to the ones that have been given.

It turns out that some people are mean a lot, some people are mean once in a while (especially after a bad day), and some people only get mean when they totally snap.  There is no simple logic to it, really. It is complicated because people are usually fairly complex.  But there are definitely the ess holes who are just angry and mean because they are unhappy, I guess.  Usually, people are only mean when something really bad has happened to them recently and they lash out without thinking.

I find that people who are mean in general tend to think that the entire world is against them.  Why they would think that, is a separate discussion, and could be a very long one because lots of different reasons can be the cause.

There are multiple possibilities. Among them, a mistake, poor judgment, insensitivity, bad mood, and the like rank high.

People are bullied because they're vulnerable and they let themselves be a target, not because of anything they've done to the bully.