The Equal Protection Clause
Amendment XIV
Section 1.
All persons born or naturalized in the United States, and subject to the jurisdiction thereof, are citizens of the United States and of the state wherein they reside. No state shall make or enforce any law which shall abridge the privileges or immunities of citizens of the United States; nor shall any state deprive any person of life, liberty, or property, without due process of law; nor deny to any person within its jurisdiction the equal protection of the laws.
This has multiple meanings, of course, but it is impossible to square any govt-mandated affirmative action decree, whether the language, intent or effect, with this express, written provision of the Constitution. So they dont even try. They just pretend it's not there.