I think the $250,000 number was probably chosen because some of the families who are not in the 2% themselves may reasonably aspire to that level of income for themselves or their kids. (That's an enormous number for an individual but for a two-income family who's in the right part of the country and especially in the right fields of employment, two six-figure incomes might not be completely out of reach, especially in the long term. And again, parents making $25K a year might have aspirations for their children.)
And with regard to sending two kids to college at $30K a year each--there was a time not that long ago when a middle-class family could send two kids to college simultaneously without anybody having to go into crushing debt. So that particular benchmark of "rich" still feels like a middle-class thing to me. Of course, now it really is out of the reach of anybody but the very well off, but still, I think that might explain why people with that ability can still honestly feel that it's not part of the definition of rich.
You wrote a thought-provoking post; I wonder whether feeling rich has more to do with the safety net or financial cushion a person has than with the house they live in or the car they drive. My family's income has vacillated wildly over the past few years (all the way down to zero for a long time after the crash of 2008) and since we didn't move or buy new cars (or do anything different) during the ups, our material condition has stayed exactly the same (or worse, since the cars just keep getting older); the real and crucial difference between the ups and the downs was whether we had a financial cushion. That's what makes it possible to take a deep breath and feel at least at ease, if not rich. People who are earning $250,000 a year and spending all of it probably genuinely do not feel rich. That's due to their own choices, of course, and their life is a world away from that of someone who doesn't feel rich because they don't have a house or a car. But if they're locked into excessive mortgage payments and car payments they might feel just as stuck as a person whose payments and income are both lower. (Personally, I think that anybody in the former position has made short-sighted choices. But I'm just talking about the definition of "feeling rich," not of "being sensible."
Anyway, very well written as always, Tom!