What term suggests that an old friend has the right to criticize without causing resentment?

The term that captures the idea of an old friend having the right to criticize without causing resentment is "prerogative." This word denotes a special right or privilege that is typically associated with an individual’s long-standing relationship. In the context of friendship, an old friend earns a unique position wherein their opinions and critiques are more readily accepted. This stems from the shared history, understanding, and trust built over time.

While "privilege" might imply a special advantage, it does not necessarily communicate the interpersonal dynamics and emotional context that prerogative does. "Authority" suggests a power dynamic that may not apply to mutual friendships, and "right" is more general and lacks the nuanced connotation of familiarity that prerogative carries. Therefore, prerogative most effectively conveys the notion that an old friend's candid critique can be seen as acceptable and almost expected without harming the relationship.