I have worked with people that are similar. I believe people like that have a self-worth problem and their inflated ego is their way to protect their worth. I don't think they care much about people's opinion. People to them are only valuable for proving their "importance" and self-worth.

I am not sure what is the best way to deal with people like that. Ignore them if you can. If you have to work with him and he did something wrong, trying to prove it doesn't help. I don't think he will care about your opinion if it disagrees with his own. Instead, I try to work around them indirectly so I don't have to deal with the games they play for a sense of importance. .