Finally understand it.
Whatever it once was, now it's the conceit expressed by some Americans that their country is better than other ones; and which is received by people in other countries as a manifestation of self-regard.
Self-complimenting is rarely an appealing characteristic. Unfortunately, as a form of self-expression, the notion of exceptionalism also conceals a xenophobic commentary that, in contrast, other countries lack the shiny and elevated qualities which America commands. In saying America is the greatest country on earth or that it is a city shining on a hill, what a person is saying is that other places aren't as good.
This is vanity. And vanity tends to crowd out genuine compliments from abroad. Why would anyone fuel another country's self-regard?
It's a shame that it is expressed as it is, when it could so easily be put less chippily: America pursues its own path, intends to do good, is proud of its achievements, believes in its own ideals and, like other countries, is unique. It is only the comparative sense that makes the notion odious and which may be used to justify acts which a less unequal country would not contemplate.
Let America be good, without insisting it must be better.
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