What people are concerned about is that we, as humans, are the thing that is disturbing the balance at the moment.
The thing is that Earth is constantly shifting in unpredictable ways. There was an interesting paper recently published working to reconstruct the temperature record of the last 500 million years. [1]
The paper concluded that global mean temperatures varied (over time) in a range from 11c to 36c. We're currently around 15. And temperature is but one of countless variables, most all of which are constantly changing.
This makes longterm equilibriums basically impossible because each time things change, it disrupts the existing balance and there will be new winners and new losers.
I recommend a watch, it is very well-directed too. But here is Wikipedia saying the theory has been discredited if you don’t want to spend the time on the documentary series: https://en.wikipedia.org/wiki/Balance_of_nature