It is evident that there has been moral progress in the world. This makes the argument that relativists pose to be invalid.
Relativists might say to that, that slavery is bad is just the opinion of more people now than it was before or perhaps new technology eliminated the need in today’s society for it. There are still people that believe that one race is better than another, but it is the minority so it is not heard
They may pose the argument that well if I didn’t like milk as a child and now I like milk today that is just a change in opinion. It isn’t moral progress and neither is the change from a historical episode of immorality like slavery.
The objectivist would respond with the fact that we can agree society is more morally civilized now than it did 100 years ago. Woman have rights now and that is more moral. Gay marriage is becoming legalized all over the world. There is a systematic way to deal with criminals now. Etc. Those that have the differing opinion are too closeminded to be defined as rational humans that can be moral.
You cannot account moral progress to change of opinion. Relativists will continue to bite the bullet with their it’s just a matter of opinion account but at what point is that still sufficient? Objectivists have concrete historical evidence to show that humans have made progress on determining moral truths.