A screen protector won't protect your screen from breaking when you drop it. That would be like laying a plastic bag on the windshield of your car then driving into a brick wall. Your car window would break. Your iPhone screen will break.
That's why I said "cases or screen protectors" .. cases to protect the glass from shattering, screen protectors to avoid scratches. A simple bumper plus a film can keep a phone in mint condition, but some people prefer a scratched up, ugly phone. To each their own, I guess.