In the middle of trying to refute my point, you actually completely misunderstood it and then emphasized it. It's obvious you have an agenda to defend the lunacy in the bible, so scientific facts and explanations appear to be unlikely to sway any of your unfounded opinions.
Animal populations are kept in control because of external pressures. Our population has no external pressure at this point, which is why it is expanding and will continue to do so until pressure is applied.
I used tigers as an example and I will keep using them because they're very relevant to this discussion. Many animal species existed long before we did and, yet, they failed to completely dominate the planet. It took millions of years for hominids to develop the necessary skills to change the environment in significant ways with tools, fire, and shelter. Tigers never adapted the way we did, which subjects them to the same pressures that most other species face and, therefore, limits their population growth. This is all in direct response to the stupidity you spouted earlier:
You literally stated that animal growth rates continue to increase, which makes no sense at all. If every animal population was concurrently expanding, the world would be as tightly packed as a Japanese train. For many hundreds of thousands of years, the population was stagnant because we hadn't evolved enough to control our surroundings. Therefore, we were subjected to the environment the same way all other species are subjected to it. Back to tigers - their population was not growing at the rates you suggest before we hunted them in any significant capacity because that's how they evolved. Everything from how often they needed to eat to their gestation period was in harmony with their surroundings until an external forcing function caused their decline.
Currently, the key difference between us and every other species is our ability to alter our immediate surroundings in such significant ways as to allow us to thrive in almost any condition. Surprise! That became true right around the time our population growth rate drastically increased. It takes animals hundreds or thousands of generations to adapt to a new external pressure, assuming it didn't force them into extinction, when all we have to do is wear a coat or take some Tylenol.
I feel like you must be intentionally missing the point because what I'm saying should be very obvious to even the most casual observer.