FLOTUS wore black and a mantilla (head cover) because she did not have "the privilege of white". Only queens of Catholic monarchies may meet the Pope in the Vatican wearing white, but I don't know "why" yet.
"This traditional rule holds that most women wear long black dresses with sleeves and mantillas, and only a very select handful of women ― around seven total ― enjoy an exception. These ladies have the “privilège du blanc,” or “privilege of the white,” which means they’re allowed to wear white to such events if they choose. According to the World Heritage Encyclopedia, the queens of Italy, Belgium and Spain, grand duchesses of Luxembourg, and princesses of the House of Savoy have historically been allowed to exercise the privilège du blanc at the Vatican."
Black/White
Dark/Light
Mirrors of each other.