To demean someone is to insult them. To demean is to degrade or put down a person or thing.
If you noticed the word mean in demean, that's a good clue to its meaning. To demean someone is very mean. You are demeaning your sister or brother if you run their underwear up a flagpole. A teacher could demean a student by saying "You're stupid!" To demean is to insult: no one wants to be demeaned. Insulting language is often called demeaning. We can also say a bad president demeaned his office.