The enthusiasm in China for building a larger navy is not aimed at the United States, but at the enormous, and growing, vulnerability of its maritime commerce. For example, over 80 percent of the oil China imports comes through the Straits of Malacca. This is the busiest waterway in the world (about 130 ships a day). Other nations have an interest in keeping these straights (which are the easiest way of moving between the Indian and Pacific oceans) open. Japan and South Korea, for example. Both, like China, move most of the oil, and much of their trade, through those straights. The nations immediately adjacent to the straights (Singapore, Indonesia and Malaysia) conduct joint patrols to keep pirates and terrorists under control. But if some other nation wanted to hurt China, all they have to do is block those straights. You could do that by sinking large ships in the narrowest parts of the straights, or putting a superior naval force there.
China does not want to be dependent on another nation, be it Japan, South Korea or the United States, for the safety of its maritime commerce. The only way to avoid that humiliating fate is to become the dominant regional naval power. While the Chinese see this as purely a matter of self-defense, China's neighbors see it as an attempt to impose Chinese control over "the eastern Sea" (the western Pacific, waters that China has historically seen as its own). China is not concerned about any fears its neighbors might have. The leadership in China is only concerned with the well-being of the Chinese economy (which is necessary to keep the Communist Party in power). Thus the determination to build a much larger navy.