Organising people by the colour of their skin makes exactly as much ontological sense as organising library books by the colour of their cover.

Can you see the fallacy you are doing here? The parent tried to suggest this: simply because a thing can be in a spectrum doesn't make it unworthy of being a category. You've twisted that analogy into this nonsensical book example.

It’s not a fallacy, it’s a bitter, dark joke.

It sounds like this is an analogy in support of the parent - is that the intent?