Typically, "starving of oxygen" means that there's not enough oxygen around anymore. That's how CO2 extinguishers work, for example. They literally remove enough of the oxygen to make the combustion stop.

Halon does NOT remove the oxygen, there's always plenty of it available. Instead, it stops the chain reaction.

> You also contradict yourself by first saying that halon is inert, and then that it neutralises oxide ions by swapping halogens, which is the opposite of non-reactive.

As I said, you can mix halon and oxygen, and they won't react (even if you try to ignite them). Halon is very unreactive, but it's obviously not _totally_ inert like helium.