If methane is combined later with a strongly electronegative element,
oxygen, and the electrons are permitted to relax toward more electronegative
atoms again, the stored energy is released.
In our spring model, combustion is analogous to releasing the constraints
on the ball and letting the strong spring pull it back. In this
model the spring is stronger for F than for O, so the energy released
on combustion in fluorine is greater.
One reason why all life on this planet uses a second-best oxidant,
of course, is the natural rarity of fluorine, which in turn goes
all the way back to elemental synthesis and the fact that fluorine
has an odd rather than an even atomic number.