Although no one enjoys dealing with them, everyone comes in contact with arrogant and disrespectful people from time to time. If you're not careful, encounters with these people can leave you upset and feeling stressed. It's important to remember that although rude people think very highly of themselves, most other people do not view them in the same way. There's a very good chance that this rude person has offended many other people, and it's not just you that has dealt with her disrespect and arrogance.
Ignore the person to the best of your ability when he is being rude and disrespectful. If you try to talk to him when you are upset, you will likely make the situation worse.
Decide what type of relationship you would like to have with him. For example, if he's a co-worker, you probably want to be able to tolerate him in the office. When interacting with him, make a peaceful working relationship your goal. You might want to avoid any conversation with him that doesn't involve work, at least at first.
Stay calm when talking to the person. An arrogant person enjoys upsetting you to the point where you say things that you don't mean or start to behave in a disrespectful manner that mimics her own behaviour.
Discuss the behaviours exhibited by him that upset you, instead of simply telling him that you find him to be a disrespectful and arrogant person. He will likely be more willing to listen to your problems with some of his specific behaviours, than thinking you have an issue with him as a person.
Be true to yourself and your beliefs and don't back down when the arrogant person tries to intimidate you. Even if she is very domineering, don't let her persuade you to do something that makes you uncomfortable.