The dreaded event will either occur or it will not. If it occurs, then the worrier suffers twice, once from the event, and once from the worry. If it does not occur, then the person suffers from neither. Therefore, worry is irrational.
This is one of my favourite logic puzzles. It's obvious that concern can be rational. Whether you worry or not might influence whether the dreaded event occurs. But it's no mean feat to translate this intuitive objection into a logically rigorous one. (Which premise is false? Or is the inference invalid?) Find out by reading my past discussions of an analogous argument, here and here.