. I'm not sure why substituting the H for an alkyl group would increase electron withdrawing capacity.
You have discovered the 'electronegativity paradox' (also known as why Pauling's electronegativity scale is wrong). Another scale of electronic effects is the Hammett scale for aromatic substituent effects. Although this does not measure electron withdrawing properties, it can reveal an ability to withdraw or donate charge. If you look at it, you will find that a methyl group is electron donating compared to hydrogen. In that case, you should expect hydrogen to be more electron withdrawing.
I have many posts on this subject including a challenge for an example of fluorine being the most electron withdrawing element, it isn't. You may find it helpful to think that electronegativity is the property your professor is asking about on the test and electron withdrawing is the property you will find in the lab. You know I ~ Br > Cl >> F, F>O>N>C, & H>C.
This entire subject is a bit complicated, but I believe I have a good explanation for the data Pauling was attempting to explain. My explanation relies upon the inverse square law (Coulomb's Law) and can explain the energy values and acidities that Pauling was attempting to explain.