Malcolm H. Watts on the cultural argument against the headcovering:
This makes nonsense of the so-called ‘cultural argument’, that the teaching of 1 Corinthians merely reflects the cultural custom of Paul’s day and that therefore it is not binding upon us in the twentieth century. The plain fact of the matter is that the apostle is here sanctioning neither Jewish nor Greek usage. He is arguing on peculiarly Christian principles that, in the worship of God, men should appear uncovered and women should appear covered. Whatever may be done in other societies, Paul insists that this is the divinely prescribed practice for Christians and that it should therefore be followed in all Christian churches.
~”Head Covering in the Worship of God,” http://www.salisburyemmanuel.org.uk/Head-covering%20in%20the%20worship%20of%20God.pdf