Fullmetal Alchemist: Brotherhood is routinely classified as one of the best anime ever made, and for good reason. Not only is it an exciting, action-packed shonen series with fabulous character development, it also has some seriously deep symbolism that adds an extra layer of intrigue.
Some symbolism seems obvious; most viewers understand the Homunculi are named after the Seven Cardinal Sins. However, it's easier to miss the way all Homunculi (aside from Gluttony) punish people who commit the sin they represent but are ultimately wiped out by the same sin.
Other bits of symbolism are more subtle, like the connection between Truth, the Gate, and a religious philosophical movement called theosophy.
Greed Judges The Greedy
Greed is a blatant incarnation of his assigned sin; he wants everything, and he’ll do whatever it takes to amass the objects of his desire. When he possesses Ling, he finds a kindred spirit - Ling’s dream of providing for his people may seem altruistic, but he isn’t looking beyond his own nation. When he promises to help May’s people, he starts to demonstrate something other than avarice.
Meanwhile, Greed himself acts in a startlingly altruistic way by sacrificing himself to save Ling from Father, weakening Father - who fancied himself a god - in the process.
Lust Judges The Lustful
Lust punishes people who exhibit her named sin. Barry the Chopper torments and slays women (who he deems weak and inferior to men), and Lust chops him to bits; a punishment to fit the sin. She uses Jean Havoc's lustful advances to manipulate him into revealing classified information about Roy Mustang, then slays him for his stupidity. Mustang, who the series implies may be a little too flirtatious with women, eventually takes out Lust.
With Lust gone, Mustang changes his ways and is more forthcoming about his romantic feelings for Hawkeye.
Wrath Is Rendered Invalid By Forgiveness
Wrath, AKA King Bradley, commits a number of vicious acts against people who exhibit rage or vengeful tendencies. The most noteworthy example of this comes when he fights Scar, who has been slaying Amestrian soldiers to exact revenge on the military organization that wiped out his people, the Ishvalans.
Scar is told if he continues pursuing his vengeance, he'll be no better than the bloodthirsty King Bradley. However, he's only truly convinced after Winry, the daughter of two of his victims, forgives him for slaying her parents.
Scar realizes he too can try to forgive, and the rest of the characters are willing to give him a second chance after his spree. Wrath's downfall is brought about when the spirit of forgiveness eliminates the values he stands for.
Sloth Is Slain By His Opposite
Sloth (the sin) is defined as laziness and as a failure to take interest in others. In FMA, Sloth attacks military officials who aren’t actually protecting their country but are instead either accepting bribes or laying around doing nothing.
Like the other homunculi, Sloth is slain by someone who represents the opposite of his sin. The Armstrong family could have easily given into this particular vice, as they come from a rich, influential family that would have had no trouble landing cushy positions of power. Instead, many members of this family care deeply about their chosen careers and work tirelessly to help others achieve their goals.