Suppose rape is commited. Is this wrong? Why?
Because I wouldn't want it to happen to me? In fact, I don't know anybody who wants to be raped. Since a prohibition against rape would therefore obviously make folks a lot happier, isn't it reasonable therefore to make laws against it?
See, simple. Laws and morality without recourse to anything more absolute than "people want to be happy."
For those that would argue that it is not wrong simply because there are no absolutes and therefore nothing is wrong to do
Woah, woah. You're talking about the cartoon version of moral relativism: "everything is right." No moral relativists hold that position. Rather we hold that since there's no accessable source of moral authority (note that there may very well be one, i.e. God, but since he rather refuses to actually tell us what he thinks, then we can't count on moral absolutes), the source of moral precepts must be society. Society therefore would be best-served by making its people as happy as possible. Good morals tend to do that, like "no rape" or "no stealing." Bad morals have the opposite effect: "women are property", "some adults may not have consensual sex with each other."
Ultimately the most rational answer is to concede that yes, there are absolute moral truths.
Except that then you have the thorny problem of trying to figure out what those moral absolutes
are. You can't just say "we'll talk about that later" because that's the most important question - not where they come from, but what they are.
Fine, there's moral absolutes. But you can't make that statement and then ignore the question "what the hell are they?"
Moral relativism is consistent with the idea that moral absolutes exist. It just says that we can't know what they are, so we approximate them via trial-and-error.