While cultures can have different activities that they find acceptable, the wrongness of the activities still apply. So: If a nation's culture believes that it is ok to beat and rape women, I challenge you to find someone outside that culture (or the women of that culture) to say it is right. Another point: We all have a similar view of what is right and what is wrong. Killing, for example, is wrong. Someone who does not believe that is usually labeled a sociopath or a psychopath.
In saying that morals are relative/subjective, you are not making the descriptive claim that different people and cultures have different morals. The majority of arguments seem to wrongly assume that this is the central claim of moral subjectivism. In claiming that morals are subjective, you are saying the these different moral judgements are all equally valid, they all accurately define right and wrong. Herein lies the central problem with subjective/relative morals.
The claim that morality is objective is compatible with the idea that different people have competing conceptions of morality. It does not, however, claim that these are all equally valid. Objective morality means that certain moral judgements are more valid than others. This seems intuitively true, for the moral judgement that murder is wrong certainly seems more true than the moral judgement that genocide is right. What can explain these moral intuitions about the different moral judgements of people? Objective morals serve as an explanation and although we may have no way of ever knowing these kind of moral truths, they still nonetheless can exist as objective truths outside of experience.
Moral objectivists argue that moral values exist independently of individual thought, that they are similar to physical facts. Moral relativism argues the opposite; right and wrong is relative to the individual/culture, man-made like the rules of a game. I agree most with the relativist point of view; we are aware that the world contains many diverse cultures and no two cultures have the same practices or ethical values. When we ask moral relativists about whether it's morally right to rape, torture, cannibalize, commit genocide, etc., they don't say then that ethics is subjective. Is that a contradiction?
What we really mean by the terms 'right', 'virtuous', and 'good' boils down to 'what I like', and what we mean by the terms 'wrong', 'evil', and 'bad' boils down to 'I like it not'. Our ethical preferences are really extensions of our aesthetic preferences. People who think violence is ugly, call it 'wrong', but people who think it is glorious do not. Most people seem to think situational contexts provides much to whether an action is 'good' or 'bad', in the same way that context or juxtaposition affect the judgment of whether a color is pretty, a smell is present, or a thing tastes good. For example, I think the violence of forcibly castrating a child is ugly, but forcibly castrating a man who just raped a child is a splendid. Likewise, I love the taste of orange juice immediately after running, but I hate the taste of orange juice immediately after brushing my teeth with mint toothpaste. (It tastes bitter.)
Just as there is a clustering of aesthetic preferences within cultures, but there is still variation, there is a similar cluster of moral concepts, but still some variation. We are more likely to approve of actions that are common and commonly accepted in the societies in which we grow up, and less likely to approve of actions that are uncommon, and commonly denigrated in the societies in which we develop.