1. We need the non-metal which does not show any positive oxidation state.

2. Check each option:

   A. Oxygen
   Oxygen usually shows oxidation state $-2$, but in compounds with fluorine, it can show positive oxidation states:

   • In $\mathrm{OF_2}$, oxygen is $+2$
   • In $\mathrm{O_2F_2}$, average oxidation state of oxygen is $+1$

   So, oxygen does exhibit positive oxidation state.

   B. Iodine
   Iodine shows several positive oxidation states such as $+1, +3, +5, +7$ in compounds like:

   • $\mathrm{ICl}$ : iodine $= +1$
   • $\mathrm{HIO_3}$ : iodine $= +5$
   • $\mathrm{HIO_4}$ : iodine $= +7$

   So, iodine does exhibit positive oxidation states.

   C. Chlorine
   Chlorine also shows positive oxidation states such as $+1, +3, +5, +7$ in compounds like:

   • $\mathrm{HOCl}$ : chlorine $= +1$
   • $\mathrm{HClO_3}$ : chlorine $= +5$
   • $\mathrm{HClO_4}$ : chlorine $= +7$

   So, chlorine does exhibit positive oxidation states.

   D. Fluorine
   Fluorine is the most electronegative element. Therefore, in all its compounds, it has oxidation state $-1$ (except elemental $\mathrm{F_2}$ where it is $0$). It never shows a positive oxidation state.

3. Therefore, the correct answer is:

$\boxed{\text{D: Fluorine}}$

4. Comparison with stored correct answer:

• Stored correct answer: $\text{D}$
• Derived answer: $\text{D}$

Hence, they agree.