Biblos writes that
extreme forms accept full holism, many adopting a cranky form of nature mysticism in which nature strives for harmony and balence.

I know what you're talking about, and some people who support this idea are kind of crazy, but it remains perfectly true that nature strives for balance.
Imbalance exists when some of the factors determining what will happen to a system are more powerful than others. When a force is stronger than the counterforce, that means something is going to happen. The system will change. After the change, two things can happen:
1) the system will be in balance
2) the system will be in imbalance
If the system is in balance, nothing will change. Obviously this might be on a fairly high level: you could have plants taking solar energy, growing and putting oxygen in the air, which is consumed by animals that consume the plants and produce carbon dioxide, which the plants consume -- if their populations are constant and the system is sustainable, this can fairly be called "no change."
If the system is in imbalance, it will change some more. A system that is imbalanced will keep changing, whereas one that is balanced will stay as it is until something outside changes it (e.g., the sun stops producing solar energy). Since there are relatively few unpredictable extra-systemic influences on the earth-wide ecosystem, balanced systems remain balanced.

Where this differs from the crunchy version of that statement is in its lack of comforting friendliness. If you have a type of animal that consumes resources faster than they can be replenished and fouls its environment, the state of balance it reaches may be one of extinction. If you have one that commits wholesale destruction of biomass, well... a charred wasteland of a planet is pretty stable.