Denying the antecedent

Denying the antecedent, sometimes also called inverse error or fallacy of the inverse, is a formal fallacy of inferring the inverse from the original statement.

One way to demonstrate the invalidity of this argument form is with a counterexample with true premises but an obviously false conclusion. For example:

If you are a ski instructor, then you have a job.
You are not a ski instructor.
Therefore, you have no job.

That argument is intentionally bad, but arguments of the same form can sometimes seem superficially convincing.

Comment fallacy in denying the antecedent on Reddit to explain this fallacy. ?