tl;dr: You've been exposed to the modernized (and politically correct) interpretation of the legend. For the majority of the legend's history, it wasn't associated with women's rights.

When we read the story of a woman going into war, many of us will impose modern feminism onto the text. We can’t help but think that this must be a story that was meant to empower women to follow Mulan’s example. But as we will see, the original authors who contributed to the legend had very different motives.

As an example of how our culture influences how we (mis)interpret passages, consider the Han dynasty proverb, “Men are wolves who fear weakness; women are rats who fear strength.”

If you think this is offensive and sexist, you’re misreading it from a modern perspective. No woman from ancient China would have been insulted to be called a rat. After all, the rat is the first of the twelve zodiac animals. While a rat cannot win against a wolf in a contest of brute strength, ancient Chinese literature depicts rats as creatures that outsmart other animals, despite being small and weak.

Thus, the above proverb merely points out that men and women are different.

Now that you understand how easy it is to misunderstand a text if we read it without questioning our modern perspective, let’s take a look at the Ballad of Mulan through ancient Chinese eyes.

As a woman, Mulan was not expected to take her father's place. While there are stories about men taking their fathers' places in battle, they never became legends. After all, these are just stories about men meeting their parents' expectations. That's hardly legendary. In Chinese thought, this is a step above taking the trash out. Who expects acclaim from doing what they ought to do?

But Mulan is special because she performs a great act of filial piety when there were no such expectations placed on her.

The author of the Ballad of Mulan constructed a situation where the protagonist was expected to walk away and do nothing. This legend was designed to teach an important lesson: when you find yourself absolved of all familial duties, make up new rules for yourself to follow.

Most people who herald Mulan as a feminist jump straight to the last line of the Ballad of Mulan:

"The male rabbit’s feet go hop and skip, The females rabbit’s eyes are muddled and fuddled.

But when two hares are running side by side close to the ground, How can you tell whether I am he or she?"

In classical Chinese literature, the rabbit is commonly used as an animal whose gender is difficult to determine. When people saw a rabbit running fast, they assumed it to be a male. When a rabbit was resting, it was assumed female. But what would happen if a female rabbit decided to run alongside a male rabbit? Everyone would think of them as both being males.

This does not imply that women are indistinguishable from men. Rather, Mulan was the exception who upheld the rule. Because her cross-dressing was necessitated by extenuating circumstances, it is highly doubtful that the author of the Ballad of Mulan wanted to encourage young girls to go to war. (Unless, of course, their elderly fathers were about to be drafted by a ruthless emperor.)

If you don’t believe me, take a look at the Song of Mulan, the first known adaptation of the Ballad of Mulan. The Song concludes with these words:

If the sons of this world’s officials could display the same virtue as Mulan, Their loyalty and filial piety would not be lost. Their fame would last throughout the ages.

Who is to follow Mulan’s example? The sons of this world’s officials. In other words, Mulan was not a heroine who left an example for young girls to follow. Rather, the focus is on how men should be just as virtuous as Mulan.

Finally, it is important to note that the Song of Mulan deletes the scene where Mulan is rewarded by the emperor. Some historians have used this to argue that China's culture became slightly less patriarchal for a very brief moment in history to allow the Ballad of Mulan to be written (but the patriarchy returned shortly afterward). However, this point has been contested.

When we read the legend of Mulan, we must put it in context. There are many, many Chinese legends where the son performs a huge act of filial piety... but there is only one very obscure legend that our modern culture has chosen to glorify.

That’s right. I’m calling Mulan an obscure legend.

After the Tang dynasty, the legend of Mulan would be virtually forgotten for several hundred years. It just wasn’t considered that interesting.

But during the Ming dynasty, playwright Xu Wei brought the legend back to life. The play Mulan Joins the Army is complete with gratuitous erotica (Mulan changes clothes on stage). In fact, the play gives more attention to Mulan’s feet, the most erotic female attribute, than it does to her twelve years of military service.

Anyone who thinks Xu Wei wrote this play to endorse women’s rights knows nothing about the play and its contents. The fact that Xu Wei murdered his third wife should tell you what he thought about women.

Fortunately, this play was never performed. We only know about it because Xu Wei had the manuscript included in a selection of his favorite works to be published on the woodblock printing press toward the end of his life.

Up until this point, Mulan was still relatively obscure. I highly doubt many Chinese people read through manuscripts of unperformed plays, and the Ballad of Mulan was only known to those who studied ancient poetry.

However, copies of Xu Wei’s manuscript began to circulate among the elite. During the Qing dynasty, Chu Renhuo incorporated Mulan as a minor character in his 100-chapter novel. Because very few people had heard about Mulan at this point, most of Chu’s readers would have assumed that he invented Mulan.

In Chu’s novel Romance of Sui and Tang, the author uses Mulan to incite hatred against non-Chinese people to protest the Manchu's oppression of the Chinese. (During this time, China was under Manchu rule.)

In this novel, Mulan is initially loyal to the Tujue khan and even saves his life. However, once the khan discovers that Mulan is a woman, he tries to take her as his concubine. The message was clear: non-Chinese leaders are immoral.

A thousand years after the Ballad of Mulan was composed, Mulan finally became well known as a result of this novel. However, none of the authors who contributed to the legend up until this point created a character that would make young girls want to follow her example.

After Mulan entered the public spotlight, the legend began developing more rapidly. For this reason, I personally believe that the Qing dynasty was when Mulan finally became a legend.

The first retelling that described Mulan as a strong and independent woman was The Complete Account of Extraordinary Mulan. However, this was not published until after the author’s death. (It was discovered around 1800.)

This novel was not based on any previous retellings of the Mulan legend, but was written as a reaction against Romance of Sui and Tang. The anonymous author of The Complete Account of Extraordinary Mulan didn't want to encourage his readers to rebel against the oppressive Qing state, but sought to glorify monasticism. This novel urges the reader to withdraw from an irredeemably corrupt society. When Mulan is falsely accused, she refuses to fight for herself, but takes her own life.

The first published novel to describe Mulan as a strong and independent woman was Fierce and Filial by Zhang Shaoxian. (This was also the first novel where Mulan is a major character, and her story is based on previous retellings.) Because strength and independence were not desirable traits for women during this time, Mulan is plagued by insecurity throughout the novel. After Mulan has been away for six years, she falls into depression and begins to worry whether she will die unmarried and childless upon returning home. Women of action were despised during Mulan’s time. A Han dynasty proverb says, “A woman of influence is not to be esteemed.”

Despite the fact that Mulan defies cultural norms, the novel still argues that her actions are virtuous. By taking her father's place, she was willing to sacrifice everything for his sake. In other words, filial piety takes precedence over gender roles.

(I'm currently working on a historical fiction novel based heavily on Fierce and Filial, so I'm not going to give away the ending. Ok, if you really want to know, see the sources.)

After the fall of imperial China, retellings increasingly emphasized Mulan’s strength. The 1949 film Mulan Joins the Army conveniently forgot that the story is set during a time when the culture was still highly patriarchal. During WWII, many Chinese men had been deployed to combat the Japanese, and women needed to step into the workforce. This film inspired both men and women to rise up and reclaim their homeland.

This movie glorifies warfare. Before Mulan joins the army, she is constantly being scolded for not being more ladylike. As her story unfolds, she finds her true self (and her true love).

From 1949 onward, the legend of Mulan has continued to carry a feminist message.

The legend has changed considerably since the Ballad of Mulan was first composed over 1,500 years ago.

See below for sources.

If you haven't yet had a read of /u/Jimedorje's answer on an earlier question about Mulan, you ought to check it out, because he highlights a few key points to keep in mind about the two main versions of the Mulan story – the 6th-century Ballad of Mulan and the 17th-century Sui-Tang Romance.

1. The Ballad was written under the Northern Wei Dynasty, a foreign 'conquest dynasty' established by a Turkic group that self-identified as the Tuoba, and which favoured Buddhism (a 'foreign' religion) over native Confucian and Daoist traditions;
2. In the Ballad, Mulan is presented as having characteristics consistent with Buddhist Bodhisattvas, who are associated with many forms and could be considered gender-fluid, and can thus be read in a metaphorical light as being about the virtues of Buddhist spirituality and/or of the Tuoba's rule; and
3. Both the Ballad and the Romance emphasise Mulan's devotion to her family, a key aspect of filial piety, though this is particularly pronounced in the Romance.

In other words, the Mulan story can be read in one sense as transgressive, and in another sense as affirmative. Its transgressiveness, particularly in the Ballad, comes through principally through the work's subtle use of Buddhist cosmology, and indeed to some extent in the fact that a woman takes the role normally expected of a man. Yet at the same time there is an affirmation of the literally patriarchal family structure laid out in Confucian thought, as Mulan sacrifices herself for the sake of her family unit and especially her father, who of course would in the ideal Confucian construction be her male authority figure until she was married. This in part is also why the threat of being married off to the Khan in the Romance version is so thematically significant – Mulan remains devoted to her existing (and one might add, Han Chinese) male authority figure, rather than becoming subordinated to a new (and one might add, Inner Asian) one. Bear in mind that the Ballad was preserved in the Song Dynasty by a male author, and the Romance was written in the Qing by a male author. Their renderings of the Mulan tale remain fundamentally committed to the prevailing view of gender relations held among Chinese men.