Relativism is the position that all points of view are as valid as any other points of view, and that the individual is the measure of what is true for that person. I see a big problem with this. The following is an illustration to demonstrate it.
The setting: A thief is casing a jewelry store so he can rob it. He has entered it to check out any visible alarm settings, locks, layout, etc. In the process, he unexpectedly got involved in a discussion with the owner of the jewelry store whose hobby is the study of philosophy and he believes that truth and morals are relative.
"So," says the owner, "everything is relative. That is why I believe that all morals are not absolute, and that right and wrong is up to the individual to determine within the confines of society. But there is no absolute right and wrong."
"That is a very interesting perspective," says the thief. "I was brought up believing there was a God, and that there was right and wrong. But I abandoned all of that and I agree with you that there is no absolute right and wrong, and that we are free to do what we want."
The thief leaves the store, returns that evening, and breaks in. He has disabled all the alarms and locks and is in the process of robbing the store. That is when the owner of the store enters through a side door. The thief pulls out a gun. The owner cannot see the man's face because he is wearing a ski mask.
"Don't shoot me," says the owner. "Please take whatever you want and leave me alone."
"That is exactly what I plan to do," says the thief.
"Wait a minute. I know you. You are the man that was in the store earlier today. I recognize your voice."
"That is very unfortunate for you," says the thief. "Because now you also know what I look like, and since I do not want to go to jail I am forced to kill you."
"You cannot do that," says the owner.
"Because it is not right," pleads the desperate man.
"But did you not tell me today that there is no right and wrong?"
"Yes, but I have a family, children that need me, and a wife."
"So? I am sure that you are insured and that they will get a lot of money. But since there is no right and wrong, it makes no difference whether or not I kill you. And if I let you live you will turn me in and I will go to prison. Sorry, but that will not do."
"But it is a crime against society to kill me. It is wrong because society says so."
"As you can see, I don't recognize society's claim to impose morals on me. It's all relative. Remember?"
"Please do not shoot me. I beg you. I promise not to tell anyone what you look like. I swear it!"
"I do not believe you and I cannot take that chance."
"But it is true! I swear I'll tell no one."
"Sorry, but it cannot be true because there is no absolute truth, no right and wrong, no error, remember? If I let you live and then I leave, you will break your so-called promise because your morals and promises are relative. There is no way I can trust you. Our conversation this morning convinced me of that."
"But it is wrong to kill me. It isn't right!"
"It is neither right or wrong for me to kill you. Since truth is relative to the individual, if I kill you, that is my truth. And, it is obviously true that if I let you live I will go to prison. Sorry, but you have killed yourself."
"No. Please do not shoot me. I beg you."
"Begging makes no difference."
If relativism is true, then was it wrong for the thief to pull the trigger? Perhaps someone might say that it is wrong to take another life needlessly, but why is that wrong if there are no absolute moral standards? Others have said that it is a crime against society. But, so what? If what is true for you is simply true, then what is wrong with killing someone to protect yourself after you have robbed him? If it is true for you that to protect yourself you must kill someone, then who cares what society says -- as long as you don't get caught? Why is anyone morally obligated to conform to social norms?
Though not all relativists will behave in an unethical manner, I see relativism as a contributor to overall anarchy. Why? Because it is a justification to do whatever you want.