Fans of "The Matrix" movie trilogy have actively debated the movie's finer plot points, contradictions and twists since the first film's release in 1999. The science-fiction film -- which is set in a post-apocalyptic landscape where machines have enslaved humanity and keep them trapped inside a computer simulation of the world as we know it -- deals heavily in philosophy, religion and free will, all of which are concepts open to much theorizing and debate.
Zion Isn't Real
One theory gained footing among fans after the release of the third Matrix film, "The Matrix: Revolutions." Toward the end of this third installment, the film's protagonist, Neo, uses telekinetic powers to destroy enemy machines. He had been able to use such powers whenever he was inside the matrix, but he was not supposed to have any powers in the so-called real world. One explanation for his sudden ability to blow things up with his mind in reality is that he never left the matrix at all: the city of Zion, the base of the human resistance to the machines, is not the real world but just another layer of the matrix, which the machines designed to keep those who escape the primary matrix under control. This theory legitimizes Neo's ability to use telekinesis in what is supposed to be the real world, since it's just another computer program he can manipulate.
The theory of the architect is a bit more complicated. In the second film, Neo meets the creator of the matrix, who explains that it is actually the second version of the matrix. The first was made too perfect and the human subjects within it felt something was off. This version, the architect explains, is deliberately flawed and offers certain subjects the choice to leave it. In short, Neo, Morpheus, Trinity and the other humans who have "escaped" the matrix were allowed to do so by the machines, which have already destroyed five previous "saviors" by offering them a choice: allow Zion to be destroyed but the current savior can rebuild it, or continue their resistance, crash the matrix, and destroy all of humanity still living inside it. A common and simple rebuttal to this entire theory is that the Architect is deliberately misleading Neo to shake his faith in himself and the prophecy.
Neo is a Program
Tying in to some degree with the Architect theory is the idea that Neo himself is at least partially a computer program. As "The One" who is prophesied to save humanity from the machines, Neo was born into the matrix with the ability to change it. In this theory, Neo is thought to be a creation of the Architect as a means of securing his control loop. Neo is designed to learn about, understand, and update the matrix, and then allow the humanity in himself to die and reboot the system, thereby continuing its power over the humans trapped inside. Proponents of this theory argue that since Neo is himself part machine, he can communicate with and destroy the machines both inside and outside the matrix, explaining his real-world abilities in the third movie.
It Isn't Supposed to Make Sense
While fans of The Matrix trilogy are quick to analyze and explain away problems in the movies, detractors are just as ready to argue that the trilogy's creators, the Wachowski brothers, had no grand scheme involving philosophical and religious allegories in the films and that they abandoned any philosophical leanings for better action sequences in the two sequels. The film borrows many of its main themes from Platonic philosophy: the plot of the first movie is a modernized version of The Allegory of the Cave, which suggests that there is a world beyond what we know, and that the objects we observe are mere shadows of their true selves. Neo's storyline, the Chosen One who must sacrifice himself to save humanity, has obvious parallels in Christianity. By the third film, however, Neo is blasting machines away with his mind and while it's entertaining to watch, it's not exactly Jesus-level miracles and doesn't seem to fit with the first film's mythology or science, which makes sense if there was never an overarching plot and the Wachowskis made it all up as they went.