Question

Why does fluorine not show a disproportionation reaction?

Answer 1

Disproportionation reactions: In these type of reactions same species gets reduced and oxidised simultaneously.
For a species to participate in a disproportionation reaction, it should be able to show variables oxidation state.

Fluorine is the most electronegative atom and has extremely small size.

Electronic configuration of fluorine:

$1s^{2}2s^{2}2p^5$

Thus, fluorine readily accepts one electron to achive stable insert gas configuration. Since it is gaining one electron, it exists as $F^{-}$ ion with -1 oxidation number.

Due to its highest electronegativity, it cannot lose electron, that's why fluorine does not show variable state.