"They're two sides of the same coin," Fisher explains. "On one side, traits evolve that benefit your kin, but don't benefit you, because you're helping your siblings or cousins. On the other side, traits that benefit you but cost your neighbours don't evolve, because you're causing damage to related individuals."
I don't know if it's bad writing / missing context, or what, but the obvious answer here is that evolution benefits the species, not the individual. And genetic diversity is one of those benefits, as otherwise a single disease could wipe out everyone.