A common misconception is that only Oxygen burns objects. However, Fluorine can do this job too. Carbon dioxide can 'burn' objects too! Rather than burning, we require a new word; oxidation.
Burning means you combust something, hence you could call it combustion. In layman terms, combustion is simply very rapid oxidation. What is oxidation then?
Oxidation is the the process of being oxidized. A substance is said to beoxidized when it loses electrons to the oxidizer, or gains oxygen atoms. The oxidizer is the substance that oxidizes (or accepts the electrons that the substance gives). The most common oxidizer is Oxygen since it is so abundant. Since it is so abundant, we naturally connote oxygen to be required for burning. This is usually true because oxygen just forms so many compounds.
When things burn, they get oxidized. Complex molecules get reduced (as in become simpler and not the other 'reduction') to simpler ones. For example, wood on combustion will give carbon dioxide and water as its main products. When this happens, the molecules of the wood gets rapidly oxidized, forming carbon dioxide and water as its final components. You can technically do this with fluorine too! You just need an oxidizer.