I disagree that people who are mean to others do it because they feel bad about themselves. I have found that people who feel bad about themselves are more likely to have low self esteem.
As far as mean people go, I don't think they feel bad about anything. I don't think they have many feelings at all, especially remorse, compassion, or empathy.
Rather, they have over-inflated egos. Their self images are way too high for their own good. They actually believe they are better than anyone else. These megalomaniacs are so self absorbed that it has eaten away any speck of humanity left in them. Their egos feed their hatefulness, and their hatefulness, in turn, feeds their egos.

How do you deal with them? Good luck! Lots of good advice in previous posts.

I am going to subscribe to this thread. I would like to know how this turns out.

It's a shame you even have to deal with a problem such as this. Why can't people just behave?
Keep us posted, Kat.