Why did "Mulan" (the live action movie) not do well in China?

The simple answer: A better, more accurate version of the legend was released in China in 2009. The Disney version strayed far from the legend, and featured implausible action sequences.

The Disney story is said to be influenced by Maxing Hong Kingston's "The Woman Warrior". This book was panned by Asian American scholars as "a distorted view of Chinese culture: one that is partially based on her own experience, but mostly fictional." To paraphrase the Wiki for the book:

Benjamin R. Tong stated, based on The Woman Warrior's fictionalized elements and inaccuracies about Chinese culture and history, that Kingston manipulates her white audience by giving them what they think is Chinese culture, which in reality is only a caricature based on Western stereotypes of Chinese people.

There was also a bit of friction from Hong Kong citizens, when the movie’s star, Liu Yifei, said she backed the city’s police, who have been criticized for their use of force against pro-democracy demonstrators. Additionally, one protest tweet indicates:

Mulan specifically thank the publicity department of CPC Xinjiang uyghur autonomous region committee in the credits.

You know, the place where the cultural genocide is happening.

They filmed extensively in Xinjiang, which the subtitles call “Northwest China”

I heard that the initial audience study of Mulan live action did well in China when they did the test.

Source?

Shouldn't the Chinese audience be proud that a Hollywood studio finally made a Chinese legend film?

Probably. If they had gotten things right.

Mulan (both the original animated version and the live-action version) never did well in China.

The amount of historical inaccuracies in the live-action Mulan is ridiculous.

Hollywood still has lots of work to do, casting all Asian actors and actresses in a movie does not automatically make Mulan a good movie.

Taking a piece of Asian culture and giving it a Hollywood make-over does not always work, it has had its successes, e.g. The Last Samurai, and failures, e.g. 47 Ronin.

Hollywood anticipated that using a "serving your country" theme in Mulan would appeal to Chinese audiences, but they got it very wrong. For more details, there is a very good review of this movie on YouTube by Accented Cinema, by the title of Mulan: A Case of Failed Empowerment. I could not put it better myself.

Couple of reasons:

1. Mulan 2020 isn't really a good film. It suffers from the same flaws as Disney's other live adaptation remakes. I can go into a lot of details here, but to summarize, the originals were made by masters of their craft but are seemingly being reinterpreted by film makers (or possibly executives) that don't understand theirs, to the point where they make basic errors.

2. The film takes a steaming dump on the original legend by introducing blatantly fictional elements of a blatantly western origin (e.g: the witch character and how she is treated, Chi being a weird version of The Force) or just plain weird changes that make no sense and devalue the legend (Mulan being a ninja since early childhood)

3. Merely being pro-CCP isn't enough to guarantee that Chinese audiences will want to see your film. Conversely, many other Hollywood films that make no mention of China do very well over there.

4. The actress for the title character has come out in support of Hong Kong police during the riots, which were fueled in part by police brutality during peaceful protests. This has sparked a boycott in that area.

TL;DR: I'd argue the main contributors are (a) the pandemic, (b) being released in competition with multiple other Mulan movies, and (c) the westernized Chinese culture.

An obvious factor here is the pandemic. Many cinemas in China had been closed for months, and when they reopened, seats looked like this:

_{A photo I took of cinema chairs in a Beijing cinema on the 24 July 2020; we can see social distancing regulations. Different cinemas had different regulations, and they eased up over time.}

I saw ??? on the 12 September 2020 in Beijing, and the social distancing requirements had eased since then. However, I feel people were not in a "business as usual" mindset: they still felt it was unsafe to go to the cinema, and people were cutting back on luxuries.

A second practical factor I think is important is that there were multiple Mulan movies released this year. In fact, when I first heard of the "new Mulan movie", I thought it referred to Matchless Mulan ????? (full movie) which appeared a few months prior. The animated Kung Fu Mulan ??????? was advertised at the same time as Disney's Mulan. Furthermore, movies are easily accessible in China without going to the cinemas, e.g. through an Internet TV, or through downloading them off the Internet (although this was the same for prior movies).

(There was several political controversies at the time, but I expect these were just minor issues.)

Beyond external factors, from critiques I've read, Chinese audiences especially hated the westernized Chinese culture. Along with other westernized movies, it is mocked using the phrase ?????? = "cultural General Tso's chicken":

???????“????”????????????????????????????????????????“??????”????????????????????????????????
During this upsurge, "cultural misappropriation" is a sensitive and hard-to-avoid topic, with "Crazy Rich Asians", "Mulan", etc., all encountering criticism from Asian audiences for Hollywood's "cultural General Tso's chicken". Westerners make seems-right-but-actually-wrong mistakes regarding Asian cultural stereotypes.
_{???????????, 12 November 2020.}

For example:

1. The idea that "one Chinese character = one word" (such as on Mulan's father's sword) is how Westerners end up with meaningless Chinese characters tattooed on their bodies: Chinese simply doesn't work like that.

2. The concept of "qi" is treated like a superpower in the movie, yet in reality it is considered something that everyone has (we might go see a doctor about it). The movie throws away Mulan's arduous hard work and bravery for "she has qi" which she possesses from childhood. Moreover, the idea that a "woman + qi = witch (which are inherently bad)" is not part of Chinese culture: everyone has qi. Chinese has a notion of ?? which is sometimes translated to "witch", but it's not the same.

   ……??????????“?”?“??”???????????????????????????????????????????????????????????????????????????“?”?????????????
   ...this movie contains the vague concepts of "qi" and "witches", as if the special point of Hua Mulan is not that she's a woman that survives in an all-male barracks, fights bravely for victory, and destroys sexual prejudice, but that she is born with the "qi" superpower and is the chosen one.
   _{Comment on Douban (5 September 2020)}

3. The concept of a phoenix rising from the ashes is not how Chinese phoenixes (??) work:

   The Fenghuang is often called the Chinese Phoenix, which makes it seem like a Chinese version of the Phoenix of Greek mythology, a bird that would repeatedly die in a burst of flames and then be reborn from the ashes, representing rebirth. This name is misleading, as the Fenghuang and Phoenix only share some superficial similarities.
   _{The Phoenix in Chinese Mythology}

I'd also guess that having an all-Chinese cast speaking English to one another is also off-putting for Chinese audiences.