If the majority of students in a school were black, the writer describes the school as diverse. If the majority of students were white, the writer described the school as not diverse. I would assume if one race makes up the majority of a school's population, it indicates a school lacks diversity. It's interesting the writer doesn't choose to see it that way.
As a white person who went to NYC schools where white people were the minority, the issue was never so much race as it was the economic differences. I think white middle class people (like this writer), have a very removed perception of minorities and the poor. They may feel pity and want to help, but they do so in the safety of their middle class position. They do not judge the poor as they would a person in their same economic position, but rather give them the brand of the oppressed and fail to acknowledge them as equals (though they believe wanting diversity is good enough). As a kid going to one of these schools--you are equals. Whatever violence, conservatism, and ignorance that pervades these communities will now be part of your life. And yes, while it's a faux pas to criticize the poor for being any of those things, going to those schools made me a part of that life as anyone born into it. I could be beat up like anyone else for wearing the wrong color shirt, yelled at for believing being gay was anything less than a sin against god (or that Jews were anything but less than human). I could watch my teachers relegated to tears as kids would take turns calling him a "fagot". I would learn to fight like everyone else to keep my bus pass, and stay away from the kids with knives in their bags.
Brooklyn isn't as bad as it used to be, but if your kid is in a classroom where the teacher spends half the time dealing with the kids acting out their behavioral issues--their education will be stunted. If the writer feels it's worth the risk for cultural integration, than that's his prerogative, but he shouldn't judge parents for wanting what's best for their children (and no going to a poor school isn't what's best for your kid--maybe it's better for society--but not your kid).