The fallacy of appeal to fear (aka argumentum in terrorem) is a type of appeal to emotion which leverages fear to reject a proposed position.

Here is an example:

Bern: "Should we go to New Orleans for our vacation?" ​Vern: "Have you not heard of Hurricane Katrina? My sister's friends' grandma drowned in New Orleans along with all five of her cats! Forget it!"

The problem here is that the mere conjuring of fear is used argumentatively, without regard to the likelihood of causes or other mitigating factors.

A general template of this fallacy would be:

1. P is frightening.

2. Therefore, P is false (or morally bad or undesirable).

The example above instantiates this template where P = "a visit to New Orleans".

This fallacy is commonly combined with a slippery slope fallacy to establish a hypothetical fear.