It's not a fallacy. The truth table for implication and its contrapositive are the same.

    A | B | A => B | ¬B => ¬A
    T | T |   T    |    T
    T | F |   F    |    F
    F | T |   T    |    T
    F | F |   T    |    T

My original point was that my parent was implicitly claiming that only living things need resources. That seemed absurd to me because of things like viruses, companies, governments, etc.

computerphage wasn't using deduction but rather contraposition. (A -> B) => (!B -> !A). The absurdity of (!B -> !A) shows that (A -> B) is not true for all cases.