Fluorine is the most electronegative element and does not exhibit variable oxidation states because:
1. It cannot expand its octet since it has no available \( d \)-orbitals.
2. Due to its high electronegativity, fluorine always assumes an oxidation state of \( -1 \) in its compounds.
Other halogens, such as bromine, iodine, and chlorine, can exhibit variable oxidation states as they possess vacant \( d \)-orbitals that allow them to expand their octet.
Final Answer:
\[
\boxed{\text{Fluorine}}
\]