If you mean on a legal level, it's less about what is gained by allowing insults than it is what is lost by disallowing them. That is, it becomes trivial to ban criticism by labeling it an insult.
On a social level, there is something to be gained from insults: authenticity. Perhaps it comes down to personal preference, but I would rather live in a society where people can speak their mind (and potentially face social backlash for it) than a society where everything is artificially sanitized. Empathy is great to strive for on a personal level, but forcing the appearance of empathy just leads to strained smiles.
On a social level, there is something to be gained from insults: authenticity. Perhaps it comes down to personal preference, but I would rather live in a society where people can speak their mind (and potentially face social backlash for it) than a society where everything is artificially sanitized. Empathy is great to strive for on a personal level, but forcing the appearance of empathy just leads to strained smiles.