[I wrote this in response to the Parents Involved case. An interesting criticism of original meaning constitutionalism from the same time (with a comment from me) can be found here.]
Public education has various purposes that separate it from education alone. Some here think parents should have free choice to send their children to the school of their choice, which they very well do have.
For instance, Pierce v. Society of Sisters held that you can send a child to parochial school. States also allow you to home school. The Supremes even held there was a constitutional right to remove an Amish child from high school (at least the last two years) if it clashed with religious principles. There also is no 'constitutional right' to send your child to the public school of your choice. Nor is there a constitutional right to dictate what the public schools teach. Sorry creation scientists and radical leftists.
This last point is important. The public school was established as a means to promote good citizenship. This means something special in this country. For instance, public schools have an open admissions policy. They cannot teach sectarian religious principles or lead students in prayer. They (should) promote American values like free inquiry and principles found in documents like the Declaration of Independence and Constitution.
And, they overall bring us all together. Once upon a time, many urban schools used the Protestant Bible, causing great Protestant/Roman Catholic divisions. Rulings such as Engel v. Vitale underlined the problems with this technique. Again, parents can send their children to religious/private schools. But, public schools provide a means of having children of all creeds coming together. For instance:
authorities have perceived public schools as an "assimilative force" by which diverse and conflicting elements in our society are brought together on a broad but common ground.
If there are limited slots, promoting such diversity in some fashion as but one factor in the selection process can be a good idea. Ditto things like neighborhood, ideology, educational level [see, e.g., a recent story thread in the comic strip "For Better or For Worse" concerning 'special needs' students] and so forth. Diversity promotes the ends of public education. If you don't like it, or don't like your kid being taught evolution or whatnot, you need not send them to public school.
The same applies to racial diversity. It is legitimate for schools to optionally promote this end, bringing together all races along with other groups.* It is not the only concern though you'd think that from some rhetoric on the other side. But, it surely can be one concern. Bringing together different groups is a core value of public education.
How can we properly understand and learn to live with fellow citizens if they are but strangers to us from early years? As with all 'different' groups, including sexual and political in nature, separation promotes prejudice, misunderstanding, and other wrongs that a diverse education can help prevent. Promoting diversity requires some recognition that we are different in some ways, or is trying to get all points of view in class illegitimate because it causes division between people inherently all alike?
The program here does in part address the problems of racial inequality. But, looking at the actual beliefs of those behind Brown, such as Thurgood Marshall, we also saw a broader version. A unifying vision of education, one in which separate but equal is not compelled just because the state did not directly cause it. In fact, it was a violation of the very principles he fought against.
Some question the means argued by the dissent here, which to me is problematic,** but worse are those who seem to miss the importance of the end. They think race conscious programs are sometimes necessary when the state mandates segregation, but not when its action allow it to go on indirectly. But, if the end result is the same, is this not akin to saying the rich and poor both cannot sleep under bridges? Equality, like the varied purposes expressed in the Preamble of the Constitution, sometimes requires, to use a phrase, affirmative action.
Surely, the state can try on their own to take a different path. At the very least, the goal is correct. Sadly, some fail even to seem to think that is true.
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* Likewise, like it or not, in some fashion segregation in fact tends to be in some fashion a result of state action ... which can very well be the active choice to not act:
"But if, after such detailed and complete public supervision, substantial school segregation still persists, the presumption is strong that the school board, by its acts or omissions, is in some part responsible."
The fact we can lie to ourselves and ignore the connection, notwithstanding.
** Economic solutions are of limited value when the problem is racial in particular. Even conservative leaning people have asked 'if not this, what?,' viewing things from a perch of watching history pass by and knowing a thing or two about education overall.