It works when people are afraid. We do have a Negativity Bias [
https://en.wikipedia.org/wiki/Negativity_bias] that gets amplified under stress.
You have to understand what you are trying push back on before telling someone who is scared - deal with it. It never works. Fears will just increase.
How else do you think we end up with 20 year wars, wall st bailouts, the TSA, the NSA, drone strikes, metal detectors at schools etc etc?
Dealing with people who are worried or panicking requires more imagination.