Almost all of the O2 in the atmosphere came from the cyanobacteria as a waste product of photosynthesis over the eons. As it happen trees, land plants and plants in general are eucaryote cells and eucaryotes have mitochondria that consume oxygen to produce energy. Cyanobacteria that happen to live in water and as there name suggest are bacteria, procaryote, therefore dont' have mitochondria. So it is so much that trees don't produce anything it's just that they also consume what they produce so their total output is marginal compared to organismes that expel all O2 as waste product.