Why isn't Fluorine, or Neon, the final electron acceptor in cellular respiration?
One of the main reasons that modern(!) biology uses oxygen as an electron acceptor is availability. 

Around 2.45 billion years ago, oxygen (O$_2$) started being built up in the atmosphere (which actually killed off a lot of the lifeforms/bacteria at that point). Since then, oxygen consuming lifeforms were able to establish themselves. Before that, most organisms probably used mainly (elemental) hydrogen as electron acceptors.

Apart from not really being available in the atmosphere, there are other reasons why fluorine or neon don't make for good biological electron acceptors:


While elemental fluorine (F$_2$) is indeed extremely electronegative, this makes it so reactive that it:
a) could not be controlled by biology [the reactivity of oxygen is why it killed so many bacteria in the first place] and
b) just does not occur (or at least remain in) in the elemental state in nature (there is no measurable F$_2$ in our atmosphere).
Neon (and other noble gases) are in theory also quite electronegative, actually so much so, that they never* occur without their electrons and therefore don't react at all.


*It's somehow possible to form noble-gas compounds, but it requires very specific chemical reaction conditions, that mostly occur under controlled man-made conditions (and are not good for biological life forms).