People don't like to hear this, but the mantilla is a symbol and a reminder that a woman is under the leadership (paternity/authority) and protection of her husband. A woman's hair is her honor. It is veiled in His Eucharistic presence. The covered head is a symbol of modesty, womanhood, maternity and sanctity. This is why the Madonna is veiled, why our sisters are veiled and why our brides and daughters on the day of their on their First Holy Communion are veiled.