Explanation:

- It is never advisable to have an axe to kill: This suggests a violent or harmful intent, typically not the intended or metaphorical use of the phrase.

- It is never advisable to have an axe to rotate: This does not make sense in context, as 'rotate' does not pair with 'axe' in idiomatic expressions.

- It is never advisable to have an axe to replace: This implies swapping out an axe, which doesn't fit the metaphorical or idiomatic use intended by the phrase.

- It is never advisable to have an axe to grind: This is a common idiomatic expression meaning to have a hidden agenda or grievance to promote, which fits the context.