What should we do? Have the US military take over the Amazon river basin, declare it a human-free zone, forcefully evict all people from the site, and let it grow back? We're not helpless, we're just not totalitarian conquerors.
I heard a story/statement once, that every time a bunch of smart people got together to think about solving the world problems, they all pretty much came up with the same solution: eugenics and birth control.
Both of these are controversial subjects at best.
Have you seen the TV show Utopia? Basically a group of people decide it's in the humanity's best interest to wipe out 90% of the population with viruses. Rather grim, but understandable in a way.
While in the domain of Sci-Fi, the solution I liked better was the idea from "Forever peace" by John Haldeman, where human evolution is propelled to the next step by increasing mutual empathy through technology. The Internet might be a small step in that direction.
The population is not stabilizing. The growth rate is stabilizing. We're still adding almost 100m new humans to the roster every year. We're going to hit 8 billion in 3 years (ahead of predictions made 20 years ago), and then 9 billion 12 years after that. People love to talk about the birth rate is falling in developed countries and how we're going to have a population peak here Real Soon Now. But I'll bet you dollars to donuts that the world human population in 2100 is greater than the population in 2090 (a horrific mass killer like the Bubonic Plague or nuclear war notwithstanding).
And yet year after year there are 80m+ more people being added. If the rate of change of the rate is slow enough it doesn't matter that it's going down, the population is still increasing at a breathtaking pace, and we'll have to have a population collapse to get back to anything sustainable.
