Papal encyclicals are written in Latin and are named after the first words of the first sentence. In the case of Paul VI's encyclical, his first sentence begins Humanae vitae tradendae munus gravissimum, "the task of perpetuating human life is an extremely weighty one." If the cult name/motto is modeled after the title of that encyclical, then it would have nothing to do with "on" or "regarding" human liberty. We can't know what that author had in mind, except to translate literally his (corrected) Latin humanae libertatis, "of human liberty ...", and hope the rest makes better sense.