But there's one more thing people don't understand about Superman, because most humans think like humans. They don't understand what it's like to be invulnerable when everyone around you ISN'T. So that's how you hurt someone who can't be injured. You go after the ones around them. Which is exactly what supervillains do best, and the core of some of Superman's best stories in history.
"Die Faltenlilien" is one of my takes on this kind of dilemma.