In 1 Corinthians 11:1-15, the Apostle Paul teaches of the proper order of the head covering in the meetings of the church.  First, he establishes proper order in verse 3, “But I would have you know, that the head of every man is Christ; and the head of the woman is the man; and the head of Christ is God.”  While this may not be a popular idea today, the scriptural order is the way the Lord intended it to be and we will receive blessings when we learn and obey God’s Word. 

Paul teaches us first about the men in verse 4 which says, “Every man praying or prophesying, having his head covered, dishonoureth his head.”  There is little debate on this point.  We still see men taking off their hats when entering the church building.  Even in public places, we see men taking off their hats/caps when prayer is being offered.  I’m sure that many men do this out of habit without even realizing that it is a scriptural principle.  What if the man refuses to uncover his head when preaching or praying?  He dishonors his head…and his head is Christ!  A man dishonors the Lord if he prays or preaches/teaches with his head covered.

In contrast to this, the woman dishonors her head if she prays or preaches/teaches with her head uncovered.  Verse 5 teaches us, “But every woman that prayeth or prophesieth with her head uncovered dishonoureth her head: for that is even all one as if she were shaven.”  What if the woman refuses to cover her head when preaching or praying?  She dishonors her head…and her head is the man!

Your question was about verse 16, so I will not discuss verses 1-15 anymore.  We have written about that topic previously and you can read that by going to this AFTB link: http://answersfromthebook.net/the-new-testament-mentions-that-women-should-cover-their-heads-when-praying-could-you-please-explain-that/  I encourage you to read this to learn how we can all honor the Lord in our actions. 

Verse 16 states, “But if any man seem to be contentious, we have no such custom, neither the churches of God.”  Paul is certainly referencing what he has previously written in this chapter.  Anticipating argument, he addresses it openly.  If any should argue that it was proper for women, in their worship, to appear like men with their heads uncovered, or men like women with their heads covered, Paul informed them that it was contrary to the teaching of the apostles and to the practice of the churches, and this teaching should be accepted without argument.  As I said, Paul anticipated resistance to this truth and sought to avoid trouble by his emphatic statement here.  Paul would later state concerning this epistle, “If any man think himself to be a prophet, or spiritual, let him acknowledge that the things that I write unto you are the commandments of the Lord.” (1 Corinthians 14:37).  What Paul writes is not his opinion, but his words are the “commandments of the Lord.” 

May we search and learn the Word of God.  May we be careful to “earnestly contend for the faith which was once delivered unto the saints.” (Jude 3).  In learning God’s Word, we are equipped to correct those who contend against the truth.  (412.6)