Morality

[DLJ]

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As a moral nihilist ( the meta-ethical view that nothing is intrinsically moral or immoral. For example, a moral nihilist would say that killing someone, for whatever reason, is neither inherently right nor inherently wrong) I hold that the holocaust is not inherently right nor wrong. Neither good nor evil.

That at best what you and other's consider good is your subjective opinion, and not a fact.

The moral realist claims that holocaust is objectively wrong.

The nihilist responds that's it not.
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The main problem with this is the weak semantics.

“nothing is intrinsically moral or immoral”:
If this is in reference to ‘a moral’ then yes, a moral would be extrinsic.
If this is in reference to ‘be moral’ then yes and no. If ‘being moral’ is in reference to knowing right from wrong, then what is “being immoral”? Knowing wrong from right?

It’s weak semantics... why not just say ‘nothing is intrinsically good or bad’?

A human can have the ability to detect a wrongness with reference to their own or a group’s ethical baseline and that would be an intrinsic/evolved ability. Rightness is unlikely to trigger any alarms.
The moral-event detecting ability is intrinsic but what is considered to be a moral event is not, it's contextual.

So, given what we know about physics, chemistry and biology, nihilism trumps essentialism (we realise that the universe doesn’t give a shit) we are also aware that “Brooklyn is not expanding” thus morality (more strictly ethics) is a social construct (in both the idea construction and the constitutive construction sense).

I recommend leaving terms like “subjective” and “objective” our the equation completely. That’s 18th century thinking and again, weak semantics.