What is the most important duty can a firefighter can do?

Save themselves! You can't help anyone else if you become disabled or killed while on scene. There is an old trick question taught at first aid lectures...

The instructors will ask "Why should you learn First Aid?" Everyone will say "So I can save someone's life." "Wrong!" says the instructor, "It's so that YOU can save your OWN life!" Same thing as firefighting- you have to available to do any good...