There's actual a lot of ambiguity about the valkyries' gender presentation. As female literary figures they often transgress typical Norse female roles and in some cases are even mistaken by the heroes for men. Kathleen M. Self explored the controversial possibility that the valkyries are meant to represent a "third gender" in her article "The Valkyrie's Gender: Old Norse Shield Maidens and Valkyries as a Third Gender" (Feminist Formations, Vol. 26, Issue 1, Spring 2014, pp. 143-172).

Most scholarship on valkyries and shield-maidens categorizes them as women, as kinds of warrior women who are connected to other, rare warrior women, such as the maiden king (meykongr) and to other women who, in exceptional circumstances, take up arms to fight [...] These discussions of valkyries and shield-maidens tend to insert them into a binary of masculine and feminine, wherein they sit somewhat uneasily in the feminine category. Yet, as other scholarship on Old Norse gender and sex has shown, the situation for all persons, not just valkyries, is much more complicated. The boundaries between masculine and feminine are not always rigid, at least insofar as women can take on masculine characteristics and receive approval, even if that approval was limited. Valkyries and shield-maidens, like the strong women of the sagas, are met with admiration, though not as paragons of femininity. As this article argues, these figures are best understood as a third gender -- a hybrid of masculine and feminine characteristics that were dominant during the time period explored.

In support of this argument, she cites several motifs in literature about valkyries and shield-maidens. Death in battle is held up as the best possible death for a man, compared to death in childbirth for a woman (both are awarded with an afterlife in Valhalla), but valkyries and shield-maidens are closely tied to death in battle. They also wear masculine-coded armour and, in a transgression of typical gender roles, select their own sexual partners which was usually limited to men. On the other hand, they are almost always referred to with feminine pronouns and words; wear jewelery; are available options for heterosexual male desire; and bear drinks for men, all coding them as female. This ambiguity only lasts until they marry men, however. Once they marry, they are "transmuted", according to Self, back into the feminine gender, leaving behind their armour and weapons to take up needlework and child-rearing:

Within these narratives, representations of valkyries and shield-maidens show that other possibilities for gender, aside from dominant forms of masculinity and femininity, were envisioned. Moreover, shield-maidens’ gender is represented as transmutable, but only in one direction—irreversibly, into the feminine gender. In doing so, they shed their agency and armor, and their social and familial networks are narrowed—networks crucial to constituting personhood in medieval Scandinavia—to the point, in many cases, where the once-independent individual was submerged into her husband’s identity. A close examination of the stories of Brynhild, Sigrún, and Sváva will show that, when in contact with the most masculine of men, the shield-maidens’ gender is altered to be more feminine.

Normally, betrothals were arranged for women by their male guardians (the only exception was that a mother could arrange her daughter's marriage if the woman's father and brothers were dead). A woman's consent was rarely legally necessary to marry. Self argues that the shield-maidens who choose their own husbands are put in the position of a man in contracting a marriage. While the shield-maiden's ability to choose her own mate is an extension of a masculine prerogative, once she is married she is slotted back into a traditional feminine role. She no longer has agency above her husband's and, in some stories, subsequent marriages are no longer under her control as her first marriage was when she negotiated it as a shield-maiden. They also take on the traditional feminine Norse role of urging men to take vengeance on their behalf instead of pursuing battle themselves as they did when they were shield-maidens. Self goes so far to describe this shift as changing genders:

It is the mixture of masculine and feminine characteristics that sets the valkyrie and the shield-maiden apart from most women and men of the eddic poems and other Old Norse literature. Their blending of attributes and actions that the ideology of gender would ideally attribute to either the masculine or feminine is what makes them a third gender. While valkyries, the more two-dimensional figures, are and remain members of the third gender, the shield-maidens do not. They change genders when they choose to marry a man—usually a man who is held up as a hero and who is the paramount example of the masculine gender. This transformation is only depicted in a small number of eddic poems [...] In each, once the shield-maiden marries, all of her masculine abilities and appearance disappear, while her feminine characteristics remain or, in a few cases, appear for the first time. Once married, she does not return to the third gender—the change is irrevocable.

Unlike shield-maidens, valkyries never marry and so never "revert" to this feminine state in spite of their sexual liasons with men. Therefore, Self asserts that "In imagining the shield-maiden or the valkyrie, these texts set up marriage as a turning point -- or, more strongly, as antithetical to their existence as a valkyrie or shield-maiden".

Self sees a stark difference between the Norse sagas and the twinned hyper-feminization and hyper-sexualization of pop-culture valkyries:

The valkyrie of a website like deviantart.com is a woman, not a hybrid of masculine and feminine. She usually has an exaggerated feminine form, her large breasts and hips contrasting with a small waist. Even when more than a few pieces of chain mail are draped across her form, her armor is form-fitted, designed to make free movement impractical, if not impossible. It is armor that is not really armor, quite unlike the mail coats of the medieval valkyrie. Instead, it feminizes her, whereas the byrnie masculinizes her medieval counterpart. Further, although depictions of violent actions are common enough and the potential for violence exists even in some of the contemporary images of the valkyrie at rest, the majority suggest that this feminine form is waiting for a man to claim it. [...] It is odd that a figure from medieval Norse myth could imagine a hybrid gender, albeit a gender that must change if the valkyrie or shield-maiden married, but is even odder that modern pop-culture images tend to place her in a narrowly defined femininity. While some of these images begin to imagine a powerful woman who possesses and uses weapons contrary to modern gender stereotypes, many fall short of this goal or else they arm a largely passive figure. Given that these images are products most likely primarily created and consumed by heterosexual men, the absence of the masculinity of the medieval valkyrie is not surprising. Although the subcultures of sci-fi, fantasy, and soft-core will probably continue to render the valkyrie in predictable and pedestrian ways, twenty-first-century scholars would do well to consider the medieval valkyrie more closely as a nuanced and even transgressive gure who can tell us something of our past and who might cast light on questions of gender, both past and present.

Now, although I've given a lot of space to Self's arguments here, they are by no means the scholarly consensus. There are three main unsettled questions here:

1. Is Self accurate in her casting of the valkyries as a third gender? Skeptics would argue that there is no clear rationale for positing a third gender among the Old Norse, especially since we have such an unusually high survival of law texts from their culture. Wouldn't these texts legislate for third-gender people if they existed as a social category?

2. Even if Self is correct to argue that valkyries and shield-maidens occupy a liminal gendered space in literature, did this trope reflect any actual gender fluidity among female warriors? While the recent archaeological claims that many Viking warrior burials are female have gotten a lot of press, there are methodological problems with the study that have left many scholars unconvinced that there were many female warriors in Viking times outside of the literary imagination.

3. If Self is right that valkyries and shield-maidens have a liminal gender but this is only a literary trope, why does the trope exist? Is it to serve as foils to the men so masculine that they can tame even a shield-maiden into feminine submission? Is it an inversion fantasy that serves to covertly solidify gender stereotypes while appearing to invert them in the name of wondrous and entertaining storytelling? Is it a means of expressing more female agency than is typically available in Norse society, whether as escapism for female listeners or revealing real-life complexities of female agency?

Self's argument that valkyries and shield-maidens were not depicted as straightforwardly feminine is sound. However, her wider conclusions bear further scholarly scrutiny. The analysis of gender in Old Norse cultures and literature is an ongoing field, so there is not yet a clear answer to any of the questions I've posed. All of this is to say that, in response to your original question about why the valkyries are depicted as female:

a) It's not universally accepted that they were depicted as unproblematically female, and b) The depiction of their gender in Old Norse texts is markedly different from the depiction of their gender in modern media.