When I came over this problem, the only time the explanation makes sense to me is if we are in protic solvent. (however, there is nothing mentioned about the solvent) Then the larger the atom of Nucleophile, the easier it is for this atom to cope with all the Hs floating around. that's why also e.g. if you compare I, Br, Cl; I will be best Nu in protic solvent, while Cl will be best in aprotic.
But I am not sure what Electronegativity has to do here. Let's see what others think.