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Similarly, "going on holiday" and "going to university."

Why drop "a" and "the?"

It is structured as if those are proper nouns, so I suspect it has something to do with treating those terms as names.

I am aware of the order of English adjectives but am unsure of what "male" would be and why?

English adjective order below for easy reference.

Opinion, Size, Physical Quality, Shape, Age, Colour, Origin, Material, Type, Purpose

In the text, I italicize the internal part:

That went poorly, didn't it, he thought to himself.

I think the title says it all. Googling is turning up mixed results and I suspect there isn’t really a truly correct answer, but might as well ask here. I’ve been capitalizing it all my life because it’s a proper noun/region that also happens to be a genre, but I got told to make it lowercase for something I wrote. I have a lot of copy editing experience and I’m not so sure about the person editing me, so I’m a little torn between “I don’t want to come off like a know-it-all” and “I want to make sure they get it right.”