If I were a heavy smoker, smoking would shorten my life; that is why I do not smoke, and I expect to live a long and healthy life. Which fallacy is committed in the above argument?

The argument denies the antecedent.

Its form is: if I were a heavy smoker (P), smoking would shorten my life (Q).

The speaker then asserts not-P, that he does not smoke.

From not-P he concludes not-Q, a long and healthy life.

Denying P does not license denying Q, since Q may hold for other reasons.

Inferring not-Q from a true conditional plus not-P is denying the antecedent.