A simplistic explanation is that each electron you try to remove costs more energy, because the effective nuclear charge becomes greater. A crude analogy might be asking for money from a relative. For each dollar he gives you, the less likely he is to give you more.
Look at the tabulated ionization potentials listed on the wikipedia page. You will see that, regardless of the element, removing a second electron is always more difficult than removing a first. (And removing a third more difficult than removing a second, etc.)
http://en.wikipedia.org/wiki/Ionization_energyComparing ionization potentials of different elements is less straightforward, but generally boils down to the same kind of nuclear core charge argument.
The flaw in your argument is that Na
2+ does not equal F and Na
+ does not equal Ne. From an electron configuration standpoint, yes, but not from a nuclear core charge standpoint. If the question asked you to compare ionization potentials of these elements, you'd be correct. But it isn't, so you're not.