In Solomons' Organic Chemistry, in a section discussing leaving groups, it is stated that$-$
Among the halogens, an iodide ion is the best leaving group and a fluoride ion is the poorest: $$I− > Br− > Cl− >> F−$$ The order is the opposite of the basicity in an aprotic solvent: $$F− >> Cl− > Br− > I−$$
But the order of basicity of halides is $F->Br->Cl->I-$ so the first relation makes sense, as leaving groups must depart as weak bases.
My question is why does the order change in an aprotic solvent? What am I missing?