Fluorine, a highly electronegative halogen, consistently exhibits an oxidation state of -1 in its compounds. This fixed oxidation state differentiates fluorine from other halogens like chlorine, bromine, and iodine, which display variable oxidation states. For instance, chlorine can exist with oxidation states of -1, +1, +3, +5, and +7.
Final Answer: Fluorine is the element that does not exhibit variable oxidation states.