If oxygen has low ionization energy compared to nitrogen because one of the p-orbital is filled with two electrons, then ionization energy of fluorine should be lower than oxygen because it has two filled p-orbitals that contains two electrons each. What causes fluorine to have higher ionization ene

The atomic size of fluorine is smaller than that of oxygen resulting in increased ionization energy of fluorine

Michael Flynn's statement that "The increased nuclear charge is by far the biggest factor" is apparently not true: hydrogen has pretty high ionization energy, and helium has the highest, as one can see, http://www.800mainstreet.com/4/0004-002-Periodic.html. So, you are asking a good question, and I do not know the answer: I learned it too long ago. Apparently, for the ionization energy, the degree to which outer orbitals are filled is less important. The degree to which outer shell is filled -- is important. Therefore noble gases have highest ionization energies.

Going back a step Flourine is bigger than lithium because there are more electrons around the F nucleus, so there is more electron/electron repulsion. Fluorine is smaller that lithium because there are more protons in the F nucleus, so there is more proton/electron attraction. Both can't be right, and unless you do the math you don't know which one is. The math isn't that easy.  So you have to be told, 'A fluorine atom is smaller than a lithium atom'. Now you know the answer, you can easy trot out the reason.  That's the way it is.