Denying the Antecedent

Denying the Antecedent is a formal logical fallacy which consists of a conditional premise, a second premise that denies the antecedent of the conditional and a conclusion which denies the consequent of the conditional. The general form of the argument is:

P1. If P, then Q

P2. Not P

C. Therefore, not Q

Since P was never asserted as the only sufficient condition for Q, other factors could account for Q. Therefore, the argument is deductively invalid.

For example:

P1. If Queen Elizabeth is an American citizen, then she is a human being

P2. Queen Elizabeth is not an American citizen

C. Therefore, Queen Elizabeth is not a human being

With this example, both premises are true statements yet the conclusion is false. This of course is due to the fact that being an American citizen is not the only sufficient condition for being a human being. 

Wikipedia: Denying the antecedent