Question

Cooking oil catches fire when kept for long on a burning stove why

Answer 1

This is because oil has low ignition temperature (the at which the object gets on fire)as when kept on fire for long tempature the heat given to it reaches the ignition temperature and thus it gets on fire

Answer 2

Because, surprisingly, cooking oil is flammable. That is, it will catch fire if it reaches its ignition point.

Keeping cooking oil in frying pan which is on a burning stove* will eventually reach the point of ignition if it's not being used for cooking.