> Although I agree, I think it's worth asking "why not?" to introspect our own position.
Well, sure, nothing wrong with asking the question, though the direct answer is pretty trivial: Because justification is by definition about reducing one claim to another (set of) claim(s), while "my moral code says I should kill witches" is simply a synonym for "I think I should kill witches", and as such just structurally is not a justification at all (as opposed to a bad or insufficient justification) when the question is "Why do you think you should kill witches?" because it just rephrases the same claim in different words.
> But at a level above law, what is the authority that determines that killing people is absolutely wrong and not just personally repugnant to the majority of the world's population?
That question doesn't really make sense to me. What does "absolute wrong" even mean? That seems like an undefined term to me. And why would this standard of an "absolute wrong" be something that we would have any use for?
> In other places and times laws might say, for instance, that to combat overpopulation we need to euthanize those under a certain threshold of contribution.
So?!
> To fight this, we either need to come to terms with the idea that morals and laws are just a matter of personal taste, in which case there's nothing really justifying our own position either and we're just fighting for our personal preference
That's both false and kindof self-contradictory.
A major part of justification is exactly about convincing other people, or you could say "fighting for our personal preference". In that regard, exactly that which convinces other people is the justification.
Another component of justification is about self-consistency and consistency with knowledge about the external world: Independently from trying to convince other people, you can try and find ways to falsify your moral claims, either by trying to find contradicting evidence in the external world, or by trying to identify internal inconsistencies within your moral framework. If you don't find any inconsistencies, that is a tentative justification for yourself.
> or we need some higher authority beyond ourselves/consensus/law that justifies our "don't kill people" position and condemns their "euthanize the parasites" position.
How would that solve anything? You just have pushed back the problem of justification to the question of why this particular authority should be the one to use as the standard, haven't you? I don't see how that would possibly be an alternative?!
> There can be no definition of moral truth within the system of morality. We need some external system to define moral truth.
That seems like a category mistake to me?! Why is moral truth something that needs to be defined, let alone defined within itself, rather than just something that needs to be discovered, and formulated as tentative conclusions subject to revision, as all empirical discovery is?