1 Corinthians 11: church: a place of respect and love

In the first century, a woman using a veil in public was showing that she was married. A single respectful woman should use a white ribbon(the vitta) on her hair. Today,  a woman uses a ring as such symbol. A woman with an uncovered hair would be seen as a prostitute. In a way, a woman with her hair covered was signaling that she is under authority. Imagine what message would women with her hair uncovered would send to the world at that time! Paul wanted them to show that they should be respected by outsiders.
The church in Corinth was taken the holy communion in a disrespectful way, as they were in a restaurant today. The wealthy people used to eat much more delicacies than the poor in holy communion (the wealthy would drink a very good wine while the poor a bad wine). Paul wanted them to show love (in holy communion) and respect (women with covered hair) for each other in the church.