If I remember my chemistry right, chlorine trifluoride would like to have a chat with you. It's such a powerful oxidizer that when burned with oxygen, the oxygen is actually the fuel rather than the oxidizer.
But then this is the stuff that the Nazis decided was too dangerous to use as rocket propellant, then decided it was too dangerous to use as a chemical weapon.
I don't want to chat with Chlorine Trifluoride, it's nasty.
But yeah, there are some obscure situations where oxygen isn't the oxidizing agent, but the name "oxidizer" gives a clue how rare that is. In most normal situations, oxygen is the oxidizer and the thing it reacts with is the fuel. Partially that's due to Oxygen being a good electron acceptor, but mostly it's because there's a lot of oxygen in the planet, and anywhere you can have humans you pretty much need to have oxygen.
