Anarchism tends to appeal to peasants because a peasants life is marked by an utter lack of control- they have no control over the weather, they have no control over prices they'll get for their crops, seed prices etc (i.e. their entire livelihood), not to mention having landlords leaning on them and various capitalist institutions bleeding them dry. Plus as technology advances companies are modifying plants so they don't seed, that way you have to buy new seeds every year- another little kick in the teeth.
The only thing peasants do have control over is the use of their land- what to plant, how to plant, when to plant, how to till, when to harvest and so on, which is why peasants are so attached to the land they till- it's the only thing they have control over. So when people advocating Soviet style collectivisation come only telling them that they should have NO control what so ever, peasants generally aren't filled with enthusiasm.
Anarchism, on the other hand, is freedom curbed only when it that freedom produces injustice. This appeals to peasants for obvious reasons, they have freedom and control over their own lives without landlords, taxes, states etc and they live in a just society.
In China the question of how to approach the peasants was obviously at the top of the agenda. In teh 1930s the population of China was roughly 500 million people, around 400 million of them being peasants (going by Mao's estimates, which I assume are as correct as can be expected given the circumstances). In order to assure victory the support of the peasants had to be won, unlike in Russia where the urban population was large and strong enough to crush peasant resistance.
This seems to have veered into 'peasants and anarchism' as opposed to 'Chinese Anarchism', a topic that I also find fascinating. It should be noted that Chinese anarchism continued to influence mainstream Chinese politics right up until Mao's death. The Ultra-Leftist Maoists that sprung up and even became dominant in some parts of China (and who were often quite popular with the peasants) during the Cultural Revolution were most certianly influenced by the history of Anarchism in China, both in their identification of the contradiction between the party and the masses and their more general approach to building Communism (building a new society in the shell of the old). I'm fairly sure there will still be some small, most likely underground, Anarchist groups in China that continue the long legacy of Anarchism in China.
"In reality, the difference is, that the savage lives within himself while social man lives outside himself and can only live in the opinion of others, so that he seems to receive the feeling of his own existence only from the judgement of others concerning him."- Jean-Jacques Rousseau
"The emancipation of the working class must be the work of the workers themselves.”- Flora Tristan
"Both those on the East and those on the West should be clear with the fact that we are not moving away from our road that we beat the path for in '48. That is to say, that we have our own ways. We always bravely say what is right on this side and what is not, and what is right on the other side, and what is not. It should be clear to everyone that we cannot be an appendage to anybody's politics, that we have our own point of view and that we know the worth of what is right, and what is not right."- Josip Tito