(worst case scenario fallacy)

A type of appeal to emotion, this fallacy occurs when someone’s position is based on an unrealistic worst-case scenario rather than what would probable or realistic. Those who argue these points do so to convince you to make a decision out of fear rather than reason by inflating the perceived cost – not the actual cost – of not accepting their position.

Examples:

What if armed terrorists were to attack your own neighborhood day-care center tomorrow morning? Are you ready to fight back? Better stock up on assault rifles!”

Maury, you should really wear a helmet when playing chess. You can easily get excited, fall off your chair, and crack your head open.

If Hell is real, then you would be wise to accept Christianity as true.