Why is fluoride the most nucleophilic halide in aprotic solvents?
When talking about elements of a group, the size of the atom is more effective than the electronegativity factor.
As $\ce{F-}$ size is too short so its electron density will be much higher than other hallogens.

In aprotic solvent the order of nucleophillicity:
$\ce{F- &gt; Cl- &gt; Br- &gt;I-}$(No hydration occurs) In protic solvant(like $\ce{H2O}$) its reversed because of hydration of ions having much electron density.