The expression “I panni sporchi non si lavano in Arno” (or more commonly, “I panni sporchi si lavano in casa”) is a golden rule regarding privacy and dignity.
The Metaphor
The saying compares private problems, arguments, or scandals to dirty underwear. Just as no one would hang their most embarrassing or soiled garments in a public square for everyone to see, family or group issues should not be shared with outsiders.
The Meaning
It is an invitation to resolve conflicts and mistakes within the environment where they originated (be it the family, the workplace, or a group of friends). Making them public only serves to fuel gossip and damage the reputation of everyone involved. In short: keep your private business private.
