Sodium metal is stored under kerosene because it:
Reacts vigorously with air and moisture
Sodium is a highly reactive alkali metal. It reacts vigorously with the oxygen and moisture present in air, often catching fire or forming sodium oxide and sodium hydroxide.
It also reacts violently with water, releasing hydrogen gas and heat, which can cause combustion.
To prevent this uncontrolled reaction with air and moisture, sodium is stored submerged in kerosene, an inert liquid it does not react with.
Thus, sodium is kept under kerosene because it reacts vigorously with air and moisture.