The Chiang Kai-Shek quote is basic 中学为体，西学为用 stuff (Chinese culture as the basis of society, Western science for technological applications) that can be traced back to the Chinese self-strengthening movement of the second half of the 19th century.
As to why Chiang did not mention that China might be on the same footing as or maybe even more advanced than the west technologically one day: I guess this has to do with the situation in the Republic of China years. Those years (from the 1911 revolution to the publication of Chiang's book in 1943 and beyond) were marked by too much internal and external conflict to seriously try to catch up with the west technologically.
Of course the ROC (on Taiwan) would later show that catching up technologically with the west was possible after all, as would South Korea. Japan had already managed to do so before Chiang even wrote his book, and mainland China did so in the decades after Chiang's death.
Re. Confucius, he is of course one of the most famous ancient Chinese philosophers. But he is also one who particularly emphasizes obedience, so it is not really surprising that an authoritarian like Xi should make use of him. In fact I believe Confucius was never really out of favour except for a few years during the cultural revolution