It's challenging when a person declares something that is obviously not true.
If a child says that the kids at school don't like him, that may be true. So in that instance, it might be worth exploring through discussion or role-playing. "Why does it seem to you that kids don't like you?" "How can you be a better friend?" Or if a person says that his friend is angry at him, you can ask "what happened?" or "what can you do next time to stop the argument or fight?" "how can you apologize to your friend?" or other questions that might lead to understanding or that might help the person realize that this is not a healthy friendship, or that perhaps he was not behaving in a friendly way or maybe it will occur to him that he simply misinterpreted the situation. In other words, self-discovery and growth towards being a better person and forming healthy relationships, which is a good thing.
However, sometimes a child states what is obviously not true. "You wouldn't let me eat ice cream for dinner. You're mean", or "You're mean to me because you made me do my homework when I was playing a video game" or "You hate me. Everyone else gets to watch that movie". In those instances you are actually parenting, instilling responsibility, or simply following your convictions (no, your 5 year old will not watch an R rated movie). You have your rules and you're sticking to them. No video games until that homework is done.
So, the inclination is to debate these types of arguments, and get the child to see the reasoning. We tend to say "no, I'm not being mean. Do you think it's mean for me to tell you to pick up your dirty clothes?" And we want to arrive at a point where the child says "ok, you're not mean. I get it."
But it's pointless. What works better is to simply state (in the form of a sentence, without an implied or stated question): "I told you to do your homework. You will not have privileges or electronics until it's done." Don't even debate the "mean" accusation. Don't dignify it with a response. If your child says "my friends all hate me", when you know that is not true, don't get into a debate. Simply state "you have nice friends" or "It was fun watching you and your friends at the playground yesterday" and walk away. If he says "dad is stupid" because dad said that there would be manners at the dinner table or because dad said there would be no cussing in the house or because dad made him go get his bike out of the driveway and put it away properly, don't ask "why is that stupid" or even say "why would you think that is stupid?". Just say something to the effect of "you will cooperate with our rules or lose the privilege of watching tv with the family (or going to the zoo next week or playing Wii with everyone or riding your bike or whatever)". No debate, no discussion. State the facts. Walk away. Unless he is developmentally challenged, he completely sees it, but the attention of debating it and the dragging-on of the discussion and seeing the frustration of the adults as they desperately try to talk about the child's feelings and soothe him so he doesn't think they're being mean is a fascinating game to play and a fun theatrical performance to direct. Don't play into it. Don't be the audience. Don't be the target. Say "you know that's not true" and leave the arena. If he persists and ramps it up (now he's crying "you're soooo mean"), simply re-state it with great calmness. "You know that's not true". Don't elaborate. He'll understand that this tactic is useless.