Rather than give a comprehensive answer, let me mention some big ideas and then you can go do some research on your own depending on what interests you more, because it seems to me that you have 2 questions: 1) "Why did [does it seem to me] Europeans dominated the oceans?" 2) "Why did the Chinese not dominate or rival the Europeans on the oceans?"
- The first one I will give 2 responses, the second of which will lead to the 2nd question. But to begin, the Europeans were in a special place in regard to technology. In the north, England, Scandinavia and the polities of the Hanseatic league faced a rough sea; the Baltic Sea was relatively calm but in order to trade outside of the Skagerrak and Kattegat, ships had to travel on the rough and unpredictable North Sea. Those participating in such trade developed technologically advanced hull designs to withstand the dangerous routes. In fact, their ships were good enough to even make it to the New World before Columbus. In the south, the Mediterranean Sea was much calmer but that also meant that wind was not as reliable. The Arabs had made a sail technology, the mizzen sail, that among many other benefits allowed ships to almost sail directly into the wind. Therefore Western Europe, in particular Spain and Portugal at first, was situated to benefit from a combination of sail and hull technology.
The second important factor is a desire to go out on the ocean. The Europeans were at the mercy of frequently hostile powers' control of trade routes to the goods of South and East Asia. There existed a high demand for these goods-- in fact other than hull technology, most of the best products, both manufactured and raw, at this time were produced outside of Europe. Hence this yearning for far away commodities and the profits associated with their trade provided a strong impetus to find a way to control importation.
2. The lack of large numbers of desirable exports in Europe was the opposite of the situation in China. The Chinese had not only almost all the raw goods they wanted like tea, silk, and nearby spice, but far superior man made items, perhaps best exemplified in pottery. In fact, when the Portuguese tried to trade their own products in East Africa about 100 years after the Chinese admiral Zheng He had visited, the locals discarded the inferior European items. So even with a 100 year head start, China did not need to trade with Europe for goods and furthermore China was the world's largest economy until almost the end of the 19th century because of its huge population, which was its own market. In other words, there was not a big economic motivation for China to learn how to dominate the oceans.
But what about Zheng He that you mentioned? He was the leader of a massive fleet of ships that went out to show off how great the Ming dynasty was. Therefore, even though China had the capability to launch a huge fleet all the way to the East African coast, the reason for doing so was not the same as the Europeans. Lastly, and perhaps most importantly due to the fact that China was the most populous, richest and technologically advanced civilization of that time, after Zheng He's voyage China culturally did not want to expand across the sea, did not want to spread its religion or culture, and in general wanted to be isolated, which it remained until forced to trade. As late as the middle of the 19th century, China still had no desire to trade with Europe outside of a few niche items like clocks. Indeed, the British, in a series of wars called the Opium Wars, had such a massive trade deficit with China that could not be overcome with normal trade that the British forced the Chinese to buy opium.
There are many, many research papers on this topic and I encourage you to go find out more, perhaps coming up with a new solution! Check Jstor and the works cited section of Wikipedia to get started. Hope you find what you are looking for.
Best,
Ivy Bridge Academy www.ivy-bridge.com