The cultural view is not arbitrary: five facts support it

(1) Paul's logic depends on head coverings having symbolic meaning already in place -- he never establishes this. (2) Paul argues from creation and nature for headship and hair length but never for the symbolic meaning of head coverings. (3) This meaning appears nowhere else in the OT or NT -- it's only a cultural reality, not a divine command. (4) Head covering symbolism is not present universally across cultures (which is why the passage is hard for modern readers). (5) Paul's pattern was to hold principles strongly while accommodating cultural differences ('all things to all people').