Nature seems to make computations that allow for a balance because, usually, breaking out of that balance has detrimental effects. Humanity's technological progress has broken us out of balance, since we're able to steal more energy than we need from our environment.

So yes, humans are obviously part of nature. That's of course where we get our primordial emotions from. But it's misleading to say we're just like other parts of nature, when that's clearly not the case. Our problem is technological progress greatly outpaces emotional development, which may or may not even be progressing. In many ways, technological progress degrades emotional development.

If you think nature is in balance, you are using much too short of timelines for your comparisons.

I am in disagreement. When nature is in an unstable situation, it rapidly seeks equilibrium. Nature spends most time in equilibrium.

Exactly, the "humans are killing machines" argument is false because all life is optimised competitively. We're definitely the best at it, but any species that evolved to our level would behave in the same way because it's fundamental to the way species evolve in general. I find it comforting and disturbing at the same time.