Question

why does edible oil shows rancidity store for a long period

Answer 1

The short answer is, we live in an oxygen-rich atmosphere, and oxygen likes to react with other things. This is called oxidation (when it’s not happening as combustion). One of the things it likes to react with is oil. We don’t like the smell that rancid (oxidated) oils produce, or the taste, so it’s probably evolutionarily advantageous for us to avoid rancid things - very likely we evolved to avoid rancid meat, which also contains oxidated fats, but our modern technologies of producing vegetable oils provide new places to sniff and taste that old, familiar, nasty rancid flavor.