I don't think that's how you lose fat. You get rid of the exhaust generated during the chemical fat burning process. If you couldn't exhale you would still burn fat.
You miss the point of the parent, which is that exhaling is not a chemical process. The point being that the CO2 you exhale is "somehow produced by something", and once it's there you have to exhale it.
That's a way of saying that breathing faster won't burn more fat just because of the breathing: burning fat is a bit more elaborate than that.