it does not always hold true as a general statement
Well then, let us try another form of syllogism to convince you. Here, we will attempt a proof by contrapositive. The original proposition can be restated as "If you bring forth progeny, then you are serving society." The contrapositive we will try to demonstrate is, therefore, "If you are not serving society, then you do not bring forth progeny."
Assumption: You do not serve society.
Definition: Society is aggregation of two or more individuals.
Restrictions: Reproduction is achieved by sexual means only.
Not serving society means not communicating with other individuals of your species. Without communication there can be no intercourse. Without intercourse there can be no sexual reproduction. Without sexual reproduction you will not bear children.
Quod erat demonstrandum