I know short answers are frowned upon in this subreddit, but the simple answer is that they didn't know that it existed, and had no reason to suspect that there was habitable land to the east. During the brief period where the Chinese were interested in marine exploration, every expedition that was sent east either came back with nothing, or never returned.

As others have pointed out, the short answer is, because China had no idea it existed. Lets dig deeper, though!

As far as I know, the idea that China discovered not only the Americas, but also Australia long before Europeans did is presented in Gavin Menzies' book 1421: The Year China Discovered the World. While the book became highly popular for its controversial hypothesis, it is not looked upon favorably by the historical community. It should be noted that Menzies is not a historian by trade and does not speak or read any form or dialect of Chinese. He was an officer in the British Royal Navy and he bases much of his ideas off of a single map and a few pieces of Chinese porcelain found in South America. His third book is about the historical evidence for the existence of Atlantis.

This is not to say that China did not have a rich history of exploration half a century before Europeans began sending ships across the Atlantic. Menzies was asserting that Zheng He, the admiral of Ming dynasty's treasure fleets, found America during one of his seven expeditions. Although some details are sketchy, we do know that Zheng He sailed mainly through the Indian Ocean and even went as far as Eastern Africa.

These expeditions were supported by the third Ming Emperor, Yongle, however... they were financed by his noble vassals. Massive resources would be taken from the provinces of Ming China to build what were sometimes 20,000 man fleets of the largest masted ships ever built. While many riches were brought back, they were claimed by the Imperial bureaucracy and not given back to the noble houses as repayment. As such, the Imperial bureaucracy grew extremely powerful and, mainly being comprised of eunuchs, there was little noble families could do to exert influence over this new powerful organization. Once Yongle died, though, the treasure fleet expeditions were called off. The superficial reason given was that China had enough on its own and did not need the rest of the world. The real reason had more to do with maintaining a political balance of power inside China.