The "northeast" quadrant are things on which education and income are associated with support for more spending. They are: "highways and bridges" and "supporting scientific research." The southwest quadrant art things on which education and income are associated with support for less spending. They are social security and "assistance to the poor." The northwest quadrant are things for which more income is associated with support for less spending and more education with support for more. That is, for most people (well-off and well educated, or low income and low education) education and income are working in different directions. They are welfare, "improving the conditions of blacks," "improving and protecting the nation's health," "improving and protecting the environment," and "improving the nation's education system." There are no items in the southeast quadrant.
So the belief that we need to cut "entitlements" is not unique to the rich--it's also more common among well educated people. This probably explains why many journalists accepted it as common sense--it's not that they had "internalized the preferences of the extremely wealthy" (as Krugman says) but that they had similar preferences to start with. As far as why, I would guess that educated people are more aware of some relevant facts--a large part of the budget is devoted to Social Security (and Medicaid), and that part is almost certain to grow because of demographic changes, so if we don't contain spending there we'll have to cut other spending, raise taxes substantially, or eventually face a debt crisis. Since journalists tend to be more familiar with these issues, I expect they are more inclined to favor cuts than educated people generally.
Krugman would presumably answer that a these facts don't mean that we need to cut entitlements: if we want people to have a long and reasonably secure retirement, which most of us apparently do, we can and should raise taxes to pay for that. There are other economists who argue that we can't actually do that--the resulting taxes would reduce economic growth so much that we'd still have to cut other spending or face a debt crisis. There are also people who focus on politics rather than economics--in practice, it's hard to raise taxes, so regardless of what we could do in principle, if spending on social security continues to increase, it will mean spending cuts on other things. In any case, opinions on this topic are not just a reflection of self-interest.