Explanation: an allegory about escaping the cycle of death and rebirth
*SPOILER ALERT!*
As others have pointed out, Buñuel himself always said he hated symbolism and hidden meanings and preferred not to give any explanations, even denying that there were any in his films at all. That does not mean, however, that his films didn't contain any. Either they were unintentionally present (which I strongly doubt), as symbols are the natural language of the subconscious and simply impossible to avoid as an artist. Or, as I suspect, they were intentionally present and he was lying about their absence because he preferred the symbols to do their work on a subconscious level, without rational analysis getting in the way of the process. Like a stage magician, Buñuel's trade as an artist is based on deception, so when he urges that there is "nothing up the sleeves", then that is the first place to look.
Many people interpret El Ángel Exterminador as a political film, an attack against the bourgeois upper class. I believe that this interpretation is wrong. Rather I see the film as purely spiritual. It is a Gnostic allegory about escaping Samsara, the continuous cycle of death and rebirth. Dream analysis often explains (a part of) a building as representing our physical body, or our Self. (cf. the expression "Elvis has left the building".) Like the characters in the film are trapped in a room of a house without knowing how and why, we are ignorant about how and why we are trapped in the incarnation of our physical existence: our bodies, our conscious Ego, etc.
The three closets in the film are important because they offer the only escape from the room. As small compartments they represent the tomb/womb of death, or more precisely the Tibetan Bardo, the state between our various lives. But like the afterlife, refuge is only temporary and the characters return (or reincarnate) back into the room, which represents life.
Closets are common symbols for the hidden parts of ourselves (like when somebody leading a double life is said to be "in the closet"), i.e. the subconscious. In Shamanic cultures, death and the subconscious are closely related. The Shamanic journey into the collective subconsciousness is likened to a journey into the Underworld and back, comparable to the journeys of mythic heroes such as Orpheus, Persephone, Heracles, Dante, Mike Hammer in the film Kiss Me Deadly and Jesus Christ, to name but a few. The dinner at the house in the film could be compared to the biblical Last Supper.
Each of the three closet doors bears a religious icon, together they form a triptych. One icon is of Saint Michael the archangel, a.k.a. the (good) angel of death, to which the angel of the title refers. Like Saint Michael, the closet door is a portal to the afterlife, the closet itself. One of the other two icons is that of the Virgin Mary with the baby Jesus. The Virgin Mary also represents a portal to the afterlife, though it would go too far beyond the scope of this post to explain exactly why. (For those who want to know more, a Google search should suffice, adding the terms "Vesica Piscis" and "birth canal".)
In the film a key is used to lock and unlock the archangel door, and at a certain moment the hidden symbolism of keys is explained: "In the cabala, a key is anything which opens the door of the unknown". Another angel, Saint Peter, (though not featured in the film) is commonly said to hold the key(s) to the gates of Heaven. I could delve further into the profound and mythological correlation between keys (or bolts) and Amanita mushrooms (the deadly Amanita virosa is also known as the "Destroying Angel", remarkably similar to the film's title), but again, that would go too far beyond the scope of this post, thus I refer to the highly fascinating works of ethnomycologists such as Robert G. Wasson, John M. Allegro and Clark Heinrich.
Three female characters return one by one from the closet behind the archangel door. Each of them tries to remember the true nature of death and/or their journey into the subconscious. Their recollections all differ, only united in their vagueness and dreamlike symbolism.
As the film progresses, the closets become increasingly more important, as does both the mention and the actual occurrence of death. When Mr. Russell dies, the closet behind the Virgin Mary door is used as his tomb. After a character remarks that a sacrifice must be made in order to escape (hence the sheep present in the house), a double suicide occurs in the third closet, the door of which bears an icon of a monk. (I'm not sure if it represents any monk in particular.) That is not enough, and the guests of the communal supper demand that their host sacrifices his life in Christlike fashion, and Mr. Nobile ("The Noble One", though spiritually rather than in worldly pedigree) is willing to comply.
There are 21 characters trapped in the room: 18 guests, the 2 hosts and the majordomo. The Masonic lodge mentioned is "Dawn [of the] Twenty One", which happens to be "a sublime column". There are 22 numbered cards in the Major Arcana of the Tarot deck (corresponding with the 22 paths between the sephiroth in the Tree of Life in the Cabala). But the last card has number 21 because the first card, The Fool, has number 0, meaning that it is not counted. It gets more interesting when the cast of the film reveals that one of the characters is simply named "Loco", or "Fool" (played by Roberto Meyer). He is the servant who triggers the magical trap by tripping over his own foot and dropping the main dish during the dinner scene. Fate is sealed before the "accident" takes place:
Fool: "And I've got to do it."
Another servant: "Because you're a clown."
Cups and pitchers feature a lot in the film, with a bit of imagination it is possible to make a connection to the Holy Grail chalice/Celtic cauldron/Mahavira vessel etc. And no doubt those with more knowledge of Freemasonry than myself could explain other elements of the film that might correlate with the myth of Hiram Abiff and the rebuilding of the temple of Solomon that represents our Self.
--->> SPOILERS FOLLOW BELOW!! <<---
In the end, only by remembering what they did before they got trapped could they manage to escape from the room and closets. This represents the need to remember our original, divine nature (very aptly called "Home" in the film) in order to escape the cycle of birth and death. As the plot shows, the breakdown of all worldly status, conditioned values and inhibitions, and even sanity itself is required before this divine nature can be restored. To achieve this, the characters in the film apply a whole repertoire of classic magical methods such as repetitive music, dancing, fasting, drugs, mystery cults, magical hand gestures, confinement in small tomb-like spaces, witchcraft, promiscuity and animal/human sacrifice.
If you pay close attention to the funeral scene, the characters that were trapped in the house and are present at the funeral are not among those trapped in the church. By then they have mysteriously disappeared, indicating that you need to escape Samsara (the reincarnation cycle) only once. Typically for Buñuel, the clergy are trapped and clueless as well. I am left wondering about all the free people, such as the servants. Perhaps they were angels/bodhisattvas. The final riot scene could represent the Norse Ragnarök or War in Heaven between the angelic forces of good and the demonic forces of evil.
© Edward Milhuisen