Denying the Antecedent

An argument of the form

A → B.
Not A.
∴ not B

A implies B. Not A. Therefore, not B.

In a three-part hypothetical syllogism, the proper form is
A → B.
Not B.
∴ not A

In other words, since A means B, we would see B if there had been A. But we don't see B, so there cannot have been any A.

Fallacially, this would be that since A means B, there must have been A to have B. But we don't see A, so there cannot have been any B. The error is in assuming that just because we get B when when we have A, that the only way to get B is with A.

This is the converse of the fallacy of Affirming the Consequent.