Step 1: The oxidation state of an atom in a bond depends on which atom pulls the shared electrons more strongly, that is, on electronegativity. The more electronegative atom in a bond is assigned the negative oxidation state and the less electronegative partner gets the positive one.
Step 2: Fluorine is the most electronegative element in the entire periodic table, with a Pauling value of about 3.98. Because there is no element more electronegative than fluorine, fluorine can never be forced to give up electron density to a partner atom. In every compound it forms, whether HF, OF2, or NaF, fluorine keeps a full negative charge on itself, so its oxidation state is always minus 1, and 0 in the free element F2.
Step 3: Compare with the other elements. Oxygen is highly electronegative but is beaten by fluorine, so in OF2 oxygen is forced into a rare plus 2 state, meaning oxygen can occasionally show a positive state. Chlorine is less electronegative than oxygen and fluorine, so in oxoacids and oxides such as HClO4 or Cl2O7 chlorine shows positive oxidation states up to plus 7. Carbon is only moderately electronegative and readily shows both negative states (as in CH4) and positive states (as in CO2), so it clearly can be positive.
Step 4: Since fluorine has no atom above it in electronegativity to lose electrons to, it is the one element that never shows a positive oxidation state, confirming option C.