1 Corinthians 11 v 16


1 Corinthians 11:16 
But if any man seem to be contentious, we have no such custom, neither the churches of God. 


11:16. Paul’s fifth argument for maintaining the status quo on head- coverings came from universal church practice. Paul was not trying to foist a new behavioral pattern on the Corinthians but simply to hold the line against self-indulgent individual excess in the name of freedom. As in the case of food offered to idols (8:1-11:1), Paul dealt with the immediate issue but also put his finger on the root of the problem, the Corinthian pursuit of self-interest which was unwilling to subordinate itself to the needs of others (cf. 10:24) or the glory of God (10:31). Throwing off the head- covering was an act of insubordination which discredited God. 

Whether women today in church services should wear hats depends on whether the custom of headcoverings in the first century is to be understood as a practice also intended for the present day. Many Bible students see that for today the principle of subordination (not the command to wear hats) is the key point in this passage. The intent of the custom of women wearing hats today, for fashion, seems far different from the purpose of the custom in the first century. 

Excerpt from: 
Walvoord, J. F., Zuck, R. B., & Dallas Theological Seminary. (1983-c1985). 
The Bible Knowledge Commentary : An Exposition of the Scriptures. 
Wheaton, IL: Victor Books.