Since I, too, hate this idea that objectivism doesn't exist, I shall say my bit.
The problem with relativism isn't so much the existence of relativism, but the denial of the existence of objectivisim. Take the three following quotations, which gives a
relatively good example of what I mean here:
The debate existing at all disproves your points.
because the option exist to debate what is heroic proves heroism is subject.
I still struggle to understand why you need a objective moral reason to not murder someone
Here's the problem: just because people have differing opinions doesn't mean that there cannot be objective standards to matters. It simply means people aren't in agreement over what that objective standard is.
A person who believes in objectivity is someone who believes there is an actual answer to the question. In contrast, a person who does not believe in objectivity must fall back to the idea that all answers are equal in value, and hence worthless.
Furthermore, relativism without objectivism is self-contradictory. If you say heroism has no objectivity, that becomes an objective statement. Hence we can make objective conclusions on heroism and thus heroism can be veiwed in an objective manner.
In general, I would argue the fact a debate exists on it at all leans more towards proof that something is objective rather than subjective, because it implies the people participating in the debate have
some form of reason to do so.