Middle class used to mean 2 separate things.
1) You made a certain income.
and
2) you were able to support a particular life style on that salary( detached house, 2 cars, vacations, able to put your kids through school), or what every your definition of middle class was.
The problem is that with inflation on some of these things, notably houses and university, someone who is middle class by definition 1 ins't middle class by definition 2.
Here is the original piece that the article is commenting on:
http://www.nytimes.com/2015/01/29/upshot/why-obamas-proposal...
For what its worth I tend to agree with the original article.
With Montessori (private school) for 2 kids, a nice house in a good neighborhood in a big city, and the fact that I reinvest all my money back into my company it certainly feels like I'm living a middle class lifestyle.
I also completely agree that you can't use just salary as your measure of middle class. It looses meaning when comparing small town to a city like NY.