Its a great movie quote, but I always found it a bit grating used outside that context, because, well, other animals dont instinctively develop some natural equilibrium with the surrounding environment.

Its not like a wolf will realize that they’ve been reproducing too much for the local population of prey animals and decide to have fewer cubs, or actively avoid certain prey species that have declining numbers compared to the rest, if theres too many to support the excess ones will simply starve, or wander off in search of prey. The rabbits wont decide to reproduce less if something happens to the local predator population, they simply overeat their food supply until their numbers collapse back down or their abundance causes the number of predators to rise.

The equilibrium is a product of every species acting in a way that would upset that balance if they were not all in competition with eachother, and it is only stable over relatively short periods of time, in the long run it changes under pressure from geological and climactic shifts, evolutionary adaptation, etc. All humans have done, is evolve an adaptation that is too disruptive for this process to look the way it normally does. (namely enough intelligence and aptitude for tool use to effectively adapt to different conditions much faster than the time it would take for anything slower breeding than perhaps a single celled organism to evolve a counter for).

Id be willing to bet that, if you gave any other animal a set of traits that effectively allowed them to adapt to things much faster than the pace of natural evolution, you would get similar disruption.

What’s more, such an equilibrium will eventually come back. If humans manage to destroy our natural life support system enough to go extinct? Then it will return as whatever survives our mass-extinction event fills empty niches and carries on as it has. If humans do survive but manage to make large scale civilization impossible and must revert to low tech subsistence hunter-gathering? Then they would be subject to the same growth constraints and competition as other large omnivores. If humans develop technology and infrastructure that allows for high tech industrial civilization to exist with a generally sustainable resource cycle, that doesnt disrupt the surrounding ecosystem anymore? Then that surrounding ecosystem is no longer subject to our disruption. If humans develop technology and infrastructure that just replaces by brute force the natural systems that we rely on, so as to no longer need them to survive, and continue on until the whole natural ecosystem is gone? Then as humans and their pets, crops, livestock, parasites etc would represent the whole of life remaining on earth, that built environment would be the environment, and as it would have to have been made generally self-sufficient and stable to get to that point, it would still represent a stable ecological state, if a very different and less diverse one than what exists now.

That doesnt mean that things wont change anymore once a stable state is reached, even stable environments in nature are not permanent, but humans cant logically continue to diminish a finite natural environment forever. Eventually humans will stop doing that, there wont be any humans to do it, or there wont be a natural environment left to do it to. In that sense, we can be viewed the same as any other disruption caused by any other organism, we’ve just created a much bigger shock than usual and the process of finding a stable state is still ongoing.