Dreams feel personal; they happen inside your head, where no one else is watching. The 1999 film The Matrix, though, is built on the ideas that dreams happen to everyone, all at once. They’re mass produced – which means that your most private thoughts are put there by someone else.

Four years ago, one of the directors of The Matrix, film-maker Lana Wachowski, came out as a transgender woman. This week, her sister and co-director, Lily Wachowski, did the same in an interview with the Windy City Times.

As Parker Molloy points out at Flavorwire, there’s a “delicious irony” in the fact that the directors of The Matrix are trans women. That’s because The Matrix is one of the most celebrated cultural touchstones of the men’s rights movement – and MRAs hate transgender women. Molloy quotes MRA adherents describing the creeping danger of men transitioning to women and warning all good MRAs to “push back against transsexualism before it infects those who you love and care about”.

It’s certainly satisfying to imagine the horror of MRAs discovering that their beloved Matrix was created by two transgender women. But rewatching the Matrix, it’s also uncomfortably apparent why the film might appeal to MRAs in the first place.

MRA enthusiasm for The Matrix centers on a famous scene in which Morpheus (Laurence Fishburne) offers hero Neo (Keanu Reeves) the chance to see reality as it really is. “You take the blue pill – the story ends,” Morpheus declares. “You wake up in your bed and believe whatever you want to believe. You take the red pill – you stay in Wonderland and I show you how deep the rabbit hole goes. Remember: all I’m offering is the truth. Nothing more.” MRAs refer to “taking the red pill” as the moment they realize that women control the world, and men are the oppressed underclass.

This is of course not at all what happens in the film; Neo discovers his world (or our world) is a mental construct created by malevolent computers, not by women. And yet, the MRAs aren’t wrong in seeing in the film a kind of terror of emasculation. Before Morpheus frees him, Neo works as a mild-mannered, nobody programmer named John Anderson. After taking the red pill, he discovers he’s actually a naked, dreaming slave, kept in suspension as computers harvest energy from his atrophying body. A boring, schlubby existence is analogized to complete physical, mental, and emotional servitude and decay.

In contrast, after taking the red pill, Neo becomes not just a violent, deadly martial arts expert, but literally the most important person in the world. He is the One, able to reshape the dream world and save the resistance. More, the narrative grants him a super-sexy love interest in the form of Trinity (Carrie-Anne Moss), who dutifully validates his masculine empowerment. Trinity is better-trained, more knowledgeable, and more committed than Neo, but the dreary logic of Hollywood narrative mandate that he’s (literally) the most important person in the world, while she’s relegated to tutor, helper, and love interest – more or less in that order.

Carrie-Ann Moss and Keanu Reeves in The Matrix: dutifully validating his masculine empowerment Photograph: Allstar/Warner Bros

Transgender women are sometimes accused of “enforcing the gender binary”, an argument that feminist and trans activist Julia Serano points out is “cut from the same cloth as the arguments that gays and lesbians are merely looking for an alternative lifestyle, or that bisexuals are merely sex-crazed or sexually confused”. The tired gender script in The Matrix isn’t due to the fact that the Wachowskis are transgender women. It’s just due to the fact that the film is popular action/adventure entertainment. You can find the same story in the novels of JK Rowling; Hermione is the studious, bright, dedicated, competent one, but despite that (or because of it?), some guy gets to be the title character and savior. And you can see nebbishy guys become empowered badasses in any number of superhero films directed by men. The world is made of entertainment designed for the approval of MRAs.

And in fact, you could see The Matrix itself as a buried, meta-commentary on its resolute faithfulness to its own genre. The Matrix is a group dream, much like those produced in Hollywood. Everyone lives in a manufactured world, following set gendered scripts. The rebels claim that they’re breaking free … but they do it while reading the same old lines as ever. Even the people building those dreams, such as the venomous Agent Smith, are stuck inside them too; everyone’s in the box, even those who can see the walls. Individuality is just the most seductive fiction. It doesn’t matter who you are, or what your name is, or what body you have; the Matrix has got you.

That’s a bleak vision, and one to some degree belied by the Wachowski sisters’ later work. Their most recent project, the television series Sense8, features a transgender woman protagonist, and is much bolder in addressing issues of identity and gender. Even The Matrix itself can be read more optimistically; Hannah Duvoix, for example, argues that the film includes transgender themes, and suggests that Neo’s self-discovery resonates with that of trans people. Still, the fact that MRA narratives can fit the film so neatly suggests just how omnipresent, and impersonal, certain dreams can be. MRAs might think you can just take a red pill and cast off all illusions, but the Wachowski’s The Matrix knows it’s not that easy.