Availability and applicability.
In the beginning, there was CO2. It was abundant in the atmosphere, and later, the oceans.
Fluorine and neon weren't, and so respiration evolved around what was (and is) available.
Ref.: Paeloclimatology / History of the Atmosphere.
The other point about oxygen is that it works rather beautifully both ways. Chloroplasts can easily split up CO2 and H2O into glucose and O2 with a bit of sunlight. Hemoglobin can combine both O2 and CO2 with just a little difference in partial pressure. Mitochondria can run through the citric acid cycle without getting destroyed in the process.
Once fluorine has taken hold of another atom and formed a molecule, it will be pretty hard for an organism to make it let go again, and if it does the fluorine will want to react with something, anything really, whether that's good for the organism or not.
On the other end, neon doesn't want to react with anything.
So while chemically there's a point to be made for the more energetic oxidizer, evolution / an organism is not "interested" in the energy content alone. The substance must be available, and the process must be somewhat sustainable. Oxygen ticked those boxes, fluorine and neon didn't.
Even rocket scientists, who are really looking for the most energetic compounds they can get their hands on, dropped the idea of fluorine as a propellant because it's not safe to handle in uncombined form. There's a lesson in there.