[usrusr]

Basic chemistry: the only ecosystems that can continually produce net O2 are those that permanently stash unoxidated C away (aka new fuel). This was the norm A Very Long Time Ago when plants were briefly ahead in the chemical arms race against everything that lives off decaying plant matter (and thus caused an imbalance which created the chemical energy we now use as fossil fuels). But in more recent history (e.g. anything dinosaur or younger) it only happens in very rare conditions. Peat-producing bog marshes are the rare exception now.

[naravara]

Plankton dying and falling to the bottom of the ocean probably sequesters something like .005% of atmospheric carbon a year. That was the main way carbon got yanked out of the atmosphere in the past. The problem is that the process is slooooooooow. Way too slow to keep up with our output.

[EGreg]

What about the other way, producing CO2?

[usrusr]

When the ecosystem is somehow tapping into an ancient stockpile of high energy C compounds to oxidate, sure, it will release more CO2 than it consumes. An example of such an ecosystem would be humans doing agriculture boosted with the Haber-Bosch process, which oxidates fossil fuel to capture plant nutrients from the air (even our crops are not entirely solar powered).

Chemistry is incredibly simple when you are only interested in the general inputs and outputs of a black box system.