1 Not all Chinese people eat everything
Because China is so big and diverse, it includes people who have all kinds of tastes. This gave some people the wrong impression that all Chinese people eat everything.
2 Historical food shortages
As food was short during a certain period of the Chinese modern history, some people adapted by eating whatever that can keep them alive. Some of those eating habits survived.
3 China was slow to enter the industrial age
Because China spent a lot of time in the agricultural age, people had to eat what they can find. Some eating habits remained even after China entered the industrial age.
4 China's culture remained intact
China's culture remained intact for many years. Many of the Chinese eating traditions were carried out since the days of the Chinese empire and lasted up till today as China managed to preserve its culture.
5 No religious constraints
China has been free of religious constraints that prevent people from eating certain foods. As people weren't constrained by certain food related teachings, they felt free to eat anything they wanted to try.
6 China is very diverse
China has a very large number of people who have diverse beliefs about food. The fact that the country has a very large number of people resulted in very diverse eating habits.
7 Buddhist practices
Buddhist instructions encourage people not to waste anything and to feed themselves with whatever is available in order to spare themselves.
8 Certain health benefits
Some Chinese people have certain beliefs about the health benefits of some foods and so they eat them to get those health benefits. (See How to make healthy eating unbelievably easy by Luke Durward)
9 Historical roots
Some foods eaten in China have historical roots. The shark fins, for example, was a food popular among rich people and was usually eaten to display a certain level of wealth. This habit, among many others was passed on to newer generations.
10 Beliefs about body parts
A common belief in China states that eating a certain body part of the animal helps the same part in the human body. This is one reason why some Chinese people eat all parts of an animal. (See Why many Americans eat big portions?)