because you’re biased.

Maybe, but we all are. But it seems you got it the wrong way round. I don’t think killing animals is wrong because I’m vegan. I’m vegan because the exploitation of animals and causing harm is wrong. Btw, regarding the killing of animals as wrong consequently leads to vegetarianism, not necessarily veganism.

Although many would wish we humans were superior species placed above the natural order, we’re clearly not.

Well, we developed a lot of things outside the natural order (note I’m not saying above, but outside). Like cars and clothes and computers and stuff. Naturalism is not an argument for killing animals.

opinion formed in modern, likely western, society

That is true.
Killing animals for food once might have been a necessity and normalized out of said necessity. But that necessity is gone. By the way, there are countless non-western cultures with vegetarian diets.

indigenous population or small culture following the practices of their ancestors and doing some hunting is not evil, or morally wrong

There were traditions of human sacrifice in history. Would you consider those traditions also not morally wrong if descendants of those cultures practiced these traditions today? What about bullfighting in spain?

It’s just the way the natural world was always supposed to work.

There is no „way the world is supposed to work”. There’s no plan, no nothing.