Isn't it more like "have a student body that is somewhat representative of the overall national demographic", on the basis that merit to attend elite institutions is evenly distributed?
This question was directly asked by a justice (I think Alito) in almost exactly those words. The answer he got from the UNC lawyer was "no", followed by a bunch of handwaving.
The central argument from the schools seems to be that ethnic diversity is a priori good, and providing that environment benefits all students. The cost of decreased acceptance rate for Asians is the cost to achieve this good, and is a worthwhile tradeoff because it benefits the Asians who do get in.
I don't find this argument totally specious. But I think it reduces to: "bigotry is acceptable if the benefits outweigh the costs". I don't think the Constitution finds this to be permissible.
That isn't the definition of "merit" that these colleges are looking for. Demonstrated academic performance is a part of it, to be sure, but it's not the ballgame.
e.g. https://college.harvard.edu/admissions/apply/what-we-look
Statistically, advantages along some dimensions are distributed unevenly across racial groups. That would predict differences in performance outcomes for members of racial groups within hierarchies where those advantages are selected for.
Personally, I don't think "ability to get into Harvard" is a particularly useful life skill, but I know opinions differ and I'm OK with that.