Why is veiling appropriate for women, but not men?

Saint Paul, in his First Letter to the Corinthians (11:4–5), writes: “Every man praying or prophesying with his head covered, disgraces his head. But every woman praying or prophesying with her head uncovered disgraces her head.”

Why would Saint Paul say this? Why is veiling appropriate for women, but not men? Isn’t that sexist? 
Not at all. 
In the Old Testament, the Ark of the Covenant was the dwelling place of God on Earth. This Ark contained the Life of the nation of Israel. It was always veiled by the tabernacle, or tent, built of woven layers of curtains. 
The Blessed Virgin Mary is the Ark of the New Covenant, for she bears within her Our Lord, the Life of the New Israel, the Catholic Church. Jesus, God made flesh, is brought to the world by the new Ark, Mary. 
But whereas for Mary and the Ark the veil is of fabric, Christ is not veiled by fabric: it is His humanity itself which is the veil that reveals His Divinity to the world. 
Mary, like the Ark, is veiled, because she brings forth Life. 

Jesus is divinity veiled by humanity, for He is Life.
Christian men represent Jesus, so uncovering their heads shows the veil Jesus wore, his humanity.
Christian women represent Mary, so veiling their heads shows they participate in the role Mary has, which is to bring Life into the world.

Happy veiling!