The argument isn't convincing. It relies on a tired rethorical trick: invent some syndrome, claim it is the basis for something you don't like, then taint the syndrome. It doesn't convince. And in this case, the outcome will be negative: once everyone fully realizes we're just normal animals, why not behave like them? Meat's back on the menu.
I see no problem with hunter-gatherers’ predation of wildlife, provided they act in ecological balance with their environment (and they do tend to, out of self-preservation).
That’s not the world the vast majority of us live in though. We kill on the order of 1 trillion animals every year. We’re devastating Earth’s biosphere for the sake of an unnecessary dietary choice.
We’ll reap what we sow, sooner or later.
Lions hunt and eat pretty, they also regularly kill cubs when taking over a pride. Does that make infanticide acceptable?
This argument is at least as silly as the parent's.