How is this story framed? Why does the author chose to introduce the story in this way?

This story is framed as a medical case study demonstrating the progression of mental illness in an adult male. Essentially, Lu Xun began the story this way in order to mask its true message. By presenting the story in this way, Lu Xun escaped outright condemnation and possibly incarceration and death for making bold claims against the traditional powers of his time. Interestingly, Lu Xun briefly studied medicine in Japan, so framing the story as a case study would not have been considered unusual for him.
The story itself, "The Diary of a Madman," is a critique of oppression in early twentieth-century China. Lu Xun, himself a leftist and Darwinian supporter, believed in the idea of revolution. He wanted to overthrow the hierarchical system of Confucian society, where the rich lived off the poor and wielded oppressive power.
In his short story, Lu Xun presents the case of a madman's diary in thirteen entries. In many of the entries, the "madman" contends that people in his community are trying to eat him. He writes that all "primitive people" once ate human flesh. However, he contends that some eventually stopped and became civilized: once they stopped, they "changed into real men."
Here, Lu Xun does not define the identities of the "primitive people." In fact, the madman classes his elder brother among the cannibals he must protect himself against. In the passage below, he begs his brother to change his ways.

"But if you will just change your ways immediately, then everyone will have peace. Although this has been going on since time immemorial, today we could make a special effort to be good, and say this is not to be done! I'm sure you can say so, brother. The other day when the tenant wanted the rent reduced, you said it couldn't be done."

The reference to "rent" is interesting, as it betrays Lu Xun's Marxist sensibilities. Lu Xun believed that communism was China's best hope against the inequity he witnessed in Chinese society.
When Mao came to power, he commended the then-deceased Lu Xun for his work in combating the "feudal forces and imperialism." I include a link below, where you can read Mao's speech commemorating the first anniversary of Lu Xun's death. Sadly, although Mao lauded Lu Xun and his humanist ideals, the dictator manipulated them for his own ends. According to historical records, Mao's policies killed more than 40 million Chinese citizens during the Great Leap Forward.
For Lu Xun, his short story will serve as a clarion call for freedom fighters of all ages.
http://afe.easia.columbia.edu/special/china_1900_luxun.htm

https://www.britannica.com/biography/Lu-Xun