What to do when other lie to or falsely accuse me?

I like and respect Lamar's answer, although I do not think it will work. Argument, as you describe it, is emotional, and not governed by logic or reason. Actually, neither is debate, because very few debaters realize or accept that as human beings we do not KNOW anything with certainty. Therefore they treat facts (that is, beliefs we agree to) as truth, which at the very least is questionable. What we can do is seek the best beliefs we can, according to our needs. To answer your question more directly, I don't think the situations you describe are worth involving yourself with. If they occur with your family members, though, or close friends, then you may be involved in a Double Bind. (Learn what that is, OK?) In addition, these people who argue with you probably have motives UNRELATED to the ostensible subject(s) of the argument. More likely, they want to control you, or put you in your place, or intimidate you, or force you to do things their way. I realize it sounds condescending, and I apologize, but as you get older these situations will probably not be as difficult or hurtful. Try as much as you can to smile and not take what's said personally, and let what others say roll off your back like water off a duck's back. What people say about you or to you NEVER EVER defines who you are, your worth or your importance. I believe every human life is precious. Forgive these people if you can and move on with your life, with warmth and love in your heart.