I have been working on this problem for a while now. The answer is not easy to give. It isn't necessarily difficult except for the paradox you noted. It is a bit complicated though. Which answer do you want, the one your professor expects or the one you are intuitively expecting to be correct?
Electronegativity is the source of the problem. This stemmed from Linus Pauling trying to explain why fluorine had higher than expected bond energies. The trends one must contend with is that as you go from C-C, N-N, and O-O, the bond strengths decrease, while from I-I, Br-Br, and Cl-Cl, the bond strengths increase. What is going to happen with F-F? It is neither as low as expected from the O-O bond nor as high as expected from the Cl-Cl bond. In 1932, Pauling suggested bonds contain ionic and covalent character. This supposition was brilliant in 1932, but not good science, especially as it has become taken as gospel. The Pauling electronegativity calculations do not follow the supposition of bonds being comprised of covalent and ionic components. This is to avoid a poor correlation, violation of opposites attracting, and the obvious argument that HI is covalent and HF is ionic.
If you wished, you could challenge your professor's suggestion that the fluoroalcohol is more acidic. I doubt he actually knows because if he did, the likelihood is that the iodoalcohol is more acidic. (If I am wrong, please post the pKa values. I am in constant search of examples (there are some) of fluorine being a better electron withdrawing group than Cl, Br, or I.) See my post here:
http://www.chemicalforums.com/index.php?topic=45100.0You could ask him which is a stronger acid glycolic acid (hydroxyacetic acid) or iodoacetic acid? (The less e-neg iodoacetic.)
I have suggested to students to learn that I>Br>Cl>F>O>N,H>C as electron withdrawing properties. (HI will be a stronger acid, better leaving group, and carbon a better electron donor. This will generally be correct, but not 100%, see the acetic acids.) Use the electronegativity values when discussing electronegativity. Keep them separate. The first for chemistry, the second for exams.