People's beliefs about what's right and wrong vary from culture to culture. What's right and wrong varies from culture to culture. The argument is invalid. It doesn't follow from the fact that people disagree about what's right and wrong that there is no objective truth about what's right and wrong. For people often disagree about objective matters.
People disagree about whether the Earth is round or flat.
It doesn't follow, however, that there is no objective truth about the matter. If so, give an example. If so, give an example. If so give an example. Give an example of a necessary condition.