|MadSci Network: Earth Sciences
Your question is really a very complicated one! I compliment you on coming up with such a hard question that looks so simple! While I don't think I can completely answer your question, I think that I understand what you are asking:
In the same way, living things combine oxygen with the food they eat and thus obtain energy. Even plants, which we normally don't think of as using oxygen, combine oxygen with the food they make to obtain energy. The reason that plants (in the daytime) give off more oxygen than they use is that, when they make food using the energy in sunlight, they change carbon dioxide and water into food and oxygen. But at night, plants absorb oxygen just like most other living things. In fact, I believe plants are sometimes removed from the rooms of hospital patients at night so that they don't use the patient's oxygen.
Of course, you can get energy from food, or wood, without combining them with oxygen. If you have a compost pile, you may notice that it is sometimes warm to the touch. And there are bacteria (called anaerobic) which do not use oxygen in their life processes; they are, in fact, poisoned by oxygen.
But combining food with oxygen gives much more energy than any other process for using food, so that aerobic organisms are able to use food much more efficiently than anaerobic organisms. This seems to be the main reason that large animals and plants (larger than a single cell) are even possible!
Interestingly, the very oxygen produced by green plants is what allows life to live out of the water. Until there was oxygen in the atmosphere, there could be no ozone layer, since ozone (O3) is another form of oxygen (O2). And the ozone layer is what protects life on the surface of the earth from powerful, damaging ultraviolet radiation from the sun.
Try the links in the MadSci Library for more information on Earth Sciences.