I may have read the article in the OP too quickly, but I didn't catch where she actually made the argument that private schools are indefensible. I caught some anecdotes about entitled shithead parents, and that Ivy schools accept more private school applicants.
I'll skip the 10,000 word treatise and point out the obvious: people with means tend to seek out the better things in life because they can afford it. News at 11. Education for their children is just one of those things. I'm sure there are great public schools out there, and if we had that option, we'd take a hard look at them. But unfortunately we don't, so we suck it up and pay the astronomical tuition for a school similar to the one in the article. It stings when I sign the check every year, but I sleep easy knowing it's my best investment. I'm responsible for giving my kids the tools necessary to be decent human beings and succeed in the world once they fly the coop, and the private school we chose is doing exactly that.
I'm a public shool kid. It was fine, but it didn't do much to prepare me for college, and in turn, the competive world after. I'd like my kids to be better prepared than I was.
On the diversity front, maybe it's just our school, but part of our tuition goes to support a good chunk of scholarships. There are kids from all sorts of socio economic backgrounds, and for that I am glad.