Why do women have to wear head coverings?

This is the same question a number of Christians in Corinth were asking. Hasn't Paul taught elsewhere that there is no male and female in Christ (e.g. Galatians 3:28)? Why should women cover if men don't? Or, if women do need to cover, why don't men?

Paul answers these questions by writing 1 Corinthians 11:2-16, and the first thing he does is talk about Christ.