Why active metal more corrodable than stable metal?

Answer 1

Because they combine easier with oxygen... For example, gold can be found in nature because is very stable (non reactive). And sodium or iron are more reactive, so they easily combine with oxygen, and they can't be found free in nature.

(Oxygen from air or from water is the one that causes corrosion)

Answer 2

An active metal is more likely to form an oxidative complex with oxygen (it will be oxidized). For example, FeO is a commonly formed oxidative species known as rust.