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.