Especially when comparing themselves to white Americans?
I've never heard a Chinese person express such a sentiment, not that I can recall, with one possible exception (family). But maybe such a sentiment does exist and is more widespread than I am aware of.
1. The love of education? Not when it is ordered solely to the pursuit of wealth.
2. Language and a 3000-yr old civilization? Do they really embody the highest values of this civilization merely because they speak a language in the Sinitic family of languages? Is that language superior to English with respect to its versatility in philosophy or theology? How about poetry? Or is just the felt superiority through being associated with a superior group?
3. The entrepreneurial spirit? Some Chinese are industrious and successful at making a buck in a foreign country, but is that really something to be proud of, if we take into account what they are neglecting?
4. A superior moral code or etiquette? This is questionable as well.