"...and self evident" is the important part. Both is evident after an analysis, but neither is self evident.

An example of an axiom is that "water is wet" as just by definitionsof water and wet this statement inherently and inevitably proves itself true.

Given that the concept of good and evil relies on morality which is inevitably subjective, no such statements can be axiomatic as axioms do need objective estabilishment of the truth.

You may call it a presumption and I won't have any issue with it as I agree with both statements, but they simply are not axioms.