Statement-1: The highest $\mathrm{Mn}$ fluoride is ${\mathrm{MnF}}_4$ whereas the highest oxide is ${\mathrm{Mn}}_2{\mathrm{O}}_7$.
Statement-2: The ability of oxygen to stabilise high oxidation states exceeds that of fluorine.

Fluoride cannot stabilise the high oxidation states as effectively as oxygen can. ${\mathrm{MnF}}_4$ is the highest $\mathrm{Mn}$ fluoride, whereas ${\mathrm{Mn}}_2{\mathrm{O}}_7$ is the highest $\mathrm{Mn}$ oxide.
Fluorine is unable to form multiple bonds with metals, whereas oxygen is capable of doing so. As a result, oxygen has a greater capacity than fluorine to stabilise higher oxidation states.