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.
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 faster we get people out of poverty, girls educated, and reduce child mortality, the faster we stop population growth.