Air containing oxygen is present all around us. We know that oxygen supports burning. So logically, in the presence of oxygen, even a small fire should burn down everything.
It is true that air around us contains oxygen which supports burning. However, it also contains nitrogen which doesn't support burning. Moreover, there is 78% of nitrogen and only 21% oxygen in the atmospheric air. So, even quantity wise nitrogen dominates and doesn't allow excessive burning. Of course, in the absence of nitrogen, oxygen would have dominated and everything would have been destroyed by a small fire.