The growth of the Chinese navy, seen from the Chinese point of view, is the result of China's three decades of economic growth and modernization. This economic growth depends on massive imports of raw materials, particularly oil and ores, especially iron ore. While China's economy could continue to grow without its massive exports, that economy would collapse without the imports. Thus China has gone from being classic "Continental Power" (that was not dependent on seaborne commerce), to a maritime power, that must maintain access to oceanic supply routes. Thus China needs a navy to help preserve that access.
Russia, the other great Eurasian continental power, is still one. Russia produces its own oil, and can get anything else it needs via land routes in Eurasia. Thus Russia is not overly concerned that its navy is shrinking to the size of coast guard. China, however, has to be particularly concerned with the sea routes to distant Persian Gulf and Africa. Australia is closer, but still a long sea distance away. It's not that China wants to fight a naval war, but it does want a strong enough navy to prevent any smaller, rogue, nation from interfering with Chinese shipping. For example, China's contribution to the anti-piracy patrol in the Gulf of Aden is a big deal in China. For once, the Chinese Navy is able to reach a long distance, and protect Chinese interests.
In particular, China has to worry about the Straits of Malacca (the narrow seaway providing the quickest passage between the Pacific and Indian oceans). Some 20 percent of all world trade moves through these straits. Sea traffic here is vulnerable to naval mines and sinking large ships in shallower channels. This would disrupt some traffic. Near total shutdown of the straits would cause economic disruption worldwide, and especially in China. Shipping costs would go up and there would be lots of shipping delays. Ultimate economic costs would run into the hundreds of billion dollars. China needs to stay on good terms with Singapore (the island city, populated largely by ethnic Chinese, right on the straits), and have a naval force capable to protecting the straits from any threat.
Then there is the Indian Ocean. India takes the name seriously, and considers itself the guardian of the sea routes through this vast area. This includes most of the oil coming out of the Persian Gulf (where most of the world's known oil reserves are). India needs access to that oil, as well as to African resources. India is not receptive to seeing the Chinese Navy operating nearby, but the Chinese feel they have to show up, to prepare for any contingency.
From China's perspective, the U.S. Navy is not the big threat, unless the Americans ally themselves with India, or anyone else trying to cut China's maritime supply lines.