> You say it perhaps a bit weird, but imho you are stating that there do not exist universal moral values, which is a very non-universal stance.

It’s an observation, and a very old one. Darius of Persia famously made a very similar observation in Herodotus.

> Well, the beauty is that we can make progress.

There is no such thing as progress in this realm.

> - If X can only register that system A an B are morally equal, because both systems are a system, then X misses some fundamental human abilities. That X is dangerous, because for X there is nothing wrong with Auschwitz.

No, the point is that there is no basis of comparison, not in moral terms. Of course you and I feel that way, living when and where we did. There are no “fundamental human abilities” being missed, this is just the same argument that “we feel this is wrong, so it’s bad and dangerous.

> - Also, a good question would be if one would like to exchange their moral beliefs for the Greek moral system. If not, why have a preference for a moral belief if they are all equal.

Of course not. Morals are almost entirely socialized. Nobody reasons themselves into a moral system and they cannot reason themselves out of one. It’s an integral part of their identity.

> Not saying this is you, but I think the main fallacy people run into is that they are aware of shortcomings in their moral acting. Some might excuse themself with relativism -> nihilism, but that is not what a strong person does. Most of us are hypocrite some of the time, but it doesn't mean you have to blame your moral intuition.

I do my best to follow my moral intuitions, and I am sometimes a hypocrite, but the point is moral intuitions are socialized into you and contingent on your milieu, so when you’re discussing these issues with other people who did not share the same socialization, moral arguments lose all their force because they don’t have the same intuitions. So we have to find some other grounds to make our point.