Well, with as many species as are threatened, endangered or recently extinct, we are doing damage.
We won't kill the earth though. Make it uninhabitable for modern human society, possibly.
All evidence so far points to modern capitalism being able to supply more and more food and nutrition for more and more people. The only want, aside from occasional disasters, comes in countries that are
decidedly not free and capitalist.
The prediction is simple and has been found correct time and again: Barring government intervention (a key point), economic measures increase over time.
The Ultimate Resource II
So pick what you want to measure, food per acre, calories or nutrition available per person, cost of a day's food per person, longevity, clothing, price of goods, and so on, they're always improving*.
So, no. The only way the Earth will become uninhabitable for modern society will be
if we succumb to scare tactics and allow the government to institute controls over production.
And yes, that implies that dirty environment + free capitalism still increases those factors faster than "clean" environment + great strictures on production.
And that makes people angry to think that, the way an atheist makes a Christian angry by saying, well, how can God sit there while children are raped to death?
* With a minimum granularity of 10 years, and ideally somewhat more.