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From "That’s not how it started": How "The Matrix" became a trans allegory explained by director:

Speaking with Them, Wachowski clarifies her previous comments, explaining that The Matrix was not intended to be a trans allegory when it was in production. While she acknowledges the movie's strong trans themes, she says the ideas came about naturally, without intention on her or co-director Lana Wachowski's part. Check out what Wachowski had to say below:

No, I didn’t [confirm The Matrix is a trans allegory].

Yeah, so that came from an interview I did for Disclosure. They had a bunch of Matrix questions. And the question they asked me was about Switch, who was originally written as a trans character who was male in the real world and female in the matrix. And they took that response and attached the question that everyone now references that it’s a trans allegory. And so it was slightly out of context, but I don’t sit here and put a stink up about it, because it is a trans allegory in that it was written by two closeted trans women. And so all of the things that are in it are super-duper trans. The idea of transformation, even the whole “My name is Neo, Mr. Anderson —” that idea of claiming identity, it’s undeniable.

Yeah, with all the decisions we made with that film, there’s just this burbling transness simmering below everything. So when I look back at the way that we cast those two parts, I can see how obvious it is that they’re one part in a lot of ways; that they’re two sides of the same coin. It’s not like these were conscious decisions, but more like we’re finding our way instinctively as these two closeted trans women. So all those things that your receptors are buzzing about are completely valid. When people say, “Oh, it’s a trans allegory,” it’s like, “Yeah… it is, but we weren’t like, Hey, let’s write a trans allegory .” That’s not how it started. We were like, “Hey, let’s write this action film,” and then we got our trans all over it. [ laughs ]