As we consider the moral convictions of other cultures, where certain things that we consider to be unacceptable behaviour are acceptable, it causes us to wonder why it is that we are different; why do we approve of the things we do, and disapprove of things “they” don't? Could it be that “right and wrong” are simply what the society you presently live in considers to be right and wrong? I have spoken to people who take this view very seriously; that right and wrong are simply what I can and can't get away with in the culture I live in; or what I would either be proud or ashamed to admit to others. On the other hand, the Christian view is that God determines what is right and what is wrong, and that God has created us with a sense of right from wrong; though our sense of morality is dulled by our fallen, sinful state so that we can tend to approve of what is wrong in God's eyes, and even disapprove of what is right in God's eyes.
The problem with the idea that morality is relative to our culture is that we can always disagree with the moral standards of our culture, and have a personal preference for some other law. Effectively, morality is one’s own, personal set of values. In fact, if moral relativity is true, then the law is really just the imposition of someone else’s moral preferences on you. But we need laws to govern us. If we all have different values conflicting with each other, society cannot function; it is nigh unto anarchy. Further, we really cannot judge anyone else as being right or wrong. Because right and wrong can change over time and from place to place, then all we can really say is that something is right or wrong for me, personally, at this moment in time. If someone steals your possessions or murders your dog, you can’t say that they did anything wrong, because they can say “It’s right in my eyes...” Just as you wish to say that this or that is “right in your own eyes”, irrespective of whether it’s seen as moral or immoral to someone else.
I remember hearing about a court case in which a pedophile was on trial. In his own defense he argued that in ancient cultures it was not considered wrong to have sexual relations with children. In other words, the act of pedophilia isn't objectively wrong since it was right in that culture. But unless we’re desperately trying defend moral relativism, we would all agree that pedophilia was wrong, even for that ancient culture. A thing is objectively true when it remains true regardless of whether anyone believes it or not. His personal view that pedophilia was right would not make it right; and neither is it right when an entire ancient culture approves of it. Our indignation against this man would not simply be over a difference of opinion.
Moral relativism tries to permit everything I want to do by demanding that those who have different moral preferences not impose those preferences upon me. But this is, itself, a moral imposition. It’s saying that it is wrong for you to impose your morality onto me. This is saying that there is an absolute, objective moral law that everyone must obey. Not to impose morality on others is assumed to be right, whether people agree with it or not.
A common practice in Roman culture during the first century, when Christianity was spreading, was to simply leave unwanted children to die in the cold. Yet Christians at that time would save those children and adopt them. They saw the practice of their culture as evil, just as we do. If morality is defined by what the majority of people do, then it would, by definition, be moral; and nobody could ever stand up and say that this was wrong. Likewise in Nazi Germany there were good men who opposed what was going on, and the truth about the atrocities going on were kept secret from the public, which suggests that even those doing them knew that they were evil. In our own culture there are certain practices which are common and legal, such as pornography or gambling or drunkenness; but these things are immoral and destroy lives. Many will read this and disagree, but on what basis? Should we never fight to make certain things illegal? And if we do, is it an arbitrary decision to “end a trend”? No, morality is far more complicated than what simply happens to be the norm.
Now, God made man to know right from wrong. But because our sense of right and wrong is corrupt, He also set the Law in stone for us to guide us back to the truth. All of the Law is summed up in the ten commandments, and even further again in the commands “You shall love the Lord your God” and “You shall love your neighbour”. The difference between right and wrong isn't always black and white, even when we have the Bible in our hands. There is “a time to love and a time to hate, a time for war and a time for peace” (Ecclesiastes 3:8) It takes wisdom to know how to love my neighbour. But that I ought to love my neighbour is objectively true. If a person doesn’t think so, we can rightly say that they are wrong.
Let God be true though every one were a liar, as it is written, “That you may be justified in your words, and prevail when you are judged.” (Romans 3:4)