PDF - http://lawyersforcivilrights.org/wp-content/uploads/2023/07/...
Their legal argument starts on p17 of the PDF and across pages 17 and 18 it cites Title VI of the Civil Rights Act, and points to 34 CFR §100.3(b)(2) which states universities in receipt of federal student funds:
> may not, directly or through contractual or other arrangements, utilize criteria or methods of administration which have the effect of subjecting individuals to discrimination because of their race, color, or national origin, or have the effect of defeating or substantially impairing accomplishment of the objectives of the program as respect individuals of a particular race, color, or national origin [1]
The general rule across most jursidictions is you can have a test for employment, admissions etc. that leads to a disparate impact - e.g. a tough physical fitness test that it is harder for women to pass than men - but if that can't be justified as relevant to the job or serving a valid role for the organisation, that's a problem.
To use the fitness test example, it's highly likely that the Marines applying such a test to decide who gets to train for special forces could justify such a test, but rather less likely if you're a company deciding on who to hire to write software or adminster databases or whatever.
The argument made in the complaint is that the justifications for legacy admissions policies don't work, and without a satisfactory justification, it's a breach of Title VI.
[1] https://www.ecfr.gov/current/title-34/subtitle-B/chapter-I/p...