the original Halon, does not so much displace oxygen as interfere with the combustion process.
BTW I used to have a rather large diesel motorboat that was equipped with a large Halon (the older stuff) fire extinguisher. I was working in the engine room when another person accidentally discharged the system. The agent was invisible but the sound scared the **** out of me and it costed big bucks to refill the tank but I am here to tell the story.
I'm in the same business that Steve retired from and know enough to be dangerous about halon and its replacements.
There are 2 main halons, 1301 and 1211. 1211 discharges mainly as a liquid and can be distributed throughout an enclosed area with reasonable precision. 1301 discharges as a gas, and is more difficult to precisely control. Michael is correct that the main way that halon extinguishes is by interfering with the chemical process of combustion. In something with a known volume, like an aircraft cabin, (or a boat's engine room), a system can sized to discharge enough halon to stop the fire, but not displace much of the oxygen. The standard we design and test to is 9% by volume. The standard for incendiary rounds is different, but that's a discussion for another day.