Oxygenic photosynthesis requires splitting water. It's kind of like a water wheel: to make it spin, you need a strong current. Light acts as the current, and light particles are the streams. For red dwarfs, the most common stars, the light is "cool" and weak — the streams barely move the wheel.
But even on Earth, with its bright Sun, the wheel uses only a drop of the available energy. The theoretical maximum oxygen output is thousands of times higher than what's actually produced. So complex life might be hiding unnoticed — and we should search for it around stars similar to ours.
The upper theoretical limit for oxygen production on Earth is thousands of times higher than what plants actually produce.