I've never heard a rational defense of moral relativism that made any sense. If there are no moral truths, then serial killers have done nothing wrong for example. If a moral relativist admits that there are some moral truths, then moral relativism is completely indefensible. At that point, you're just arguing over what is and what is not a moral truth.
How about the fact that all morals are made up and therefore obviously relative to those who made them up? There may be instinctual preference on many, but that doesn't make it a universal rule.
The fact the morality was invented makes it synthetic but not necessarily relative. Numbers are also "made up".
Its possible that moral truths are objective but our interpretation of these objective truths is imperfect and therefore seems relative.
To use another commenters example, the fact that killing is not morally blameworthy in some cases doesn't mean that an absolute moral truth doesn't exist but just that our concept of killing is just too broad to express it.
A moral absolutist would argue that most, or even all, are wrong in one way or another. One can be a moral absolutist without claiming to be able to evaluate the morality of any particular scenario.
To provide an analogous example, there is a two-player game called Hex for which it has been proven that there exists a dominant strategy for the first player, but a generalized winning strategy is unsolved. One can soundly assert that such a strategy exists without knowing what it is. Likewise, its not fundamentally invalid to assert that there exist absolute moral truths without knowing what they are.
Universal moral truths. Like absolutes. We can say killing is bad, but many would say killing a mass murderer currently on a murder spree would be more moral than letting them kill a bunch of people.
Just because there aren't moral truths doesn't mean a serial killer did nothing wrong. You seem to be stuck on finding a single contradiction and using that to dismiss everything else related as irrelevant. That's not actually how the world works.
Similarly in physics, the existence of non-newtonian fluids, doesn't invalidate Newton's work in fluid dynamics.
If there are no moral truths, then serial killers have done nothing wrong for example.
This is a sort of circular argument, it's premised on the notion that serial killers have done something objectively wrong.
If you start with the notion that some things are objectively wrong, then of course you'll come to the conclusion that objective morality exists, because it's one of the assumptions you started with.
It all starts with defining what morality means. The way I would define morality is behaviors that maximize flourishing for sentient creatures and minimize suffering. While it is clearly difficult to quantify flourishing and suffering, there are behaviors that clearly cause suffering in this world and impede the opportunity for flourishing and, by the above definition of morality, are plainly immoral. The way I see it, rejecting the possibility that flourishing and suffering can be quantified at all is the only argument that can be made against moral absolutism. Everything else is just quibbling over relevant variables across the spectrum of available behaviors to determine what makes them more or less moral. There is always a behavior that is objectively the more moral choice, but it might be difficult in practice to determine which is the more moral choice due to a lack of available relevant data. The absence of said data shouldn't be assumed to be because it doesn't/can't exist, but rather that it hasn't been collected. Rejecting the idea that there is always a more moral behavior amongst several choices is the dangerous assumption, imo.
Merely defining a word is semantics, and the discussion over objective vs subjective morality is about the nature of these moral claims.
Is there some karmic energy in the universe, or a god above all that judges right from wrong? That's how people often anchor their morality in an objective framework.
From a purely secular framework, morality appears to be subjective, just a set of practical rules that let creatures interact in mutually beneficial ways.
If you personally like the idea of all sentient creatures avoiding suffering, it's still a subjective preference, not a moral system that is rooted in some kind of good and bad properties that exist outside the judgment of the creatures themselves.
If there are no moral truths, then serial killers have done nothing wrong for example
This does not follow from moral relativism. Moral relativism simply states the morality of serial killers is determined by people rather than an absolute truth.
For example, if you add the detail of “serial killer of humans”, most societies would deem that morally wrong. In contrast, “serial killer of wasps” would be considered perfectly fine by many. A moral relativist would say the difference between these two is determined by society.
You can, of course, claim that murdering humans is not morally wrong. A moral absolutist might say “you’re wrong because X”, while a moral relativist might say “I don’t agree because X”.