I think that by "different walks of life" you mean different skin colors, right? Real diversity to me means people who come from different places, have been through different experiences, do different kinds of work, have read different books, have different ideas, and so on: exactly what public school can't offer.
The biggest benefit of going to a public high school in the DC area was being forced to interact with kids from almost every background you could imagine. This includes ethnicity, income bracket, intelligence, and social ability. True diversity is an education in our own human race, specifically the common bonds that unite all of us. Being able to see a wide range of perspectives and experience completely different cultural norms on a daily basis can go a long way to testing your own assumptions about the world.
This is real diversity--some single, some married, some with kids, some without, some older, some younger, coming from all different educational backgrounds, and living in different communities.
If everybody went to the same handful of colleges, is roughly the same age, and lives in the same trendy suburb, it doesn't matter what color they are. That "diversity" is literally skin-deep.
The problem is, "diversity" too often means only superficial diversity (skin color, sex) instead of actual diversity (experience, culture, language, thinking patterns, ...).
Any school will have a culture. Those that pride themselves on diversity tend to have one narrow kind of variety, and extreme monoculture on other axes - or else have a bunch of subcultural groups that don't really talk to each other. There's a kind of fundamental conservation: for people to be able to communicate and work together requires a certain level of cultural commonality.
So whichever school you went to, you end up finding it easy to talk with some number of people and hard to talk with some number of people. It all averages out. The questions that matter are a) how good or bad that culture is and b) how good or bad the non-cultural aspects of your education are.
What types of diversity can you have amongst racially, socially, and economically homogenous people? What are you talking about? What is your grand, open-minded idea that ignores what actual diversity is?
Are you asking about diversity of race only? Or diversity in general? The argument is that a more diverse student body creates a better educational environment for everyone - it broadens the experience. In addition to your academic studies, you learn about interacting with people who are different from you. People who think differently, reach different conclusions, even when confronted with the same data.
Racial diversity is only part of the equation. You also want gender diversity and class/income diversity - any of the major factors that shape how we view the world.
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