The Kohen has to take two birds, and slaughter one of them such that its blood drips into an earthenware vessel with flowing water, and dip cedar-wood, hyssop, crimson thread, and the other bird into the flowing water which is mixed with the blood of the slaughtered bird. He then sprinkles this over the metzora (“leper”) or the house seven times, after which the live bird is set free. Now the whole subject of the metzora carries tremendous morals: the Talmud says: These afflictions come because of seven things: lashon ha-ra’, blood-shed, swearing false oaths, sexual immorality, arrogance, robbery, and stinginess (Arakhin 16a).
A person who sinned by committing robbery and being stingy is condemned to sitting alone outside of the camp, thereby losing money because he is unable to work; and sometimes, his house becomes afflicted and has to be destroyed. And if he shed blood, he is reminded of this sin by having the bird’s blood sprinkled over him; he is afflicted with bodily suffering as a punishment for having afflicted bodily suffering on someone else. As a punishment for pursuing sexual immorality he becomes physically repulsive, such that no woman will want him. As a punishment for having spoken lashon ha-ra’ and thereby causing division among people, he is now divided from everyone else and dwells alone.
It goes further: he guarded his tongue neither from lashon ha-ra’ nor from swearing falsely; so the Talmud says, What makes the metzora unique, that the Torah commands him to bring two birds to purify himself? – G-d said: His actions were the actions of a chatterer, therefore the Torah enjoins him to bring [birds which are] chatterers as a sacrifice (Arakhin 16b). And for his sin of arrogance he brings the wood of the cedar tree, one of the tallest and proudest of all trees, together with hyssop, one the smallest of all plants, on which the Midrash explains: Why is the metzora cleansed with the tallest of the tall and the lowliest of the lowly?... – Because he is afflicted with tzara’at for having aggrandised himself like a cedar tree; so when he humbles himself like a hyssop, he is cured (Pesikta Rabbati, Parah 14, 60b). The sinner thereby purifies his sin which was as red as the crimson thread and makes it as white as snow. It seems to me that his arrogance is the source of all his sins, and all the other sins are a result of it, as I shall show immediately.
These two birds represent important concepts. The Torah commands him to bring two birds, live and pure (Leviticus 14:4), which the Midrash expounds upon: Rabbi Yosé the Galilean says: Specifically a bird which lives outside of town. And which bird is this? – A swallow (Sifra, Metzora 5:14). And the Sifra further says: The birds must be live, and not slaughtered; pure, and neither impure…nor non-kosher (ibid. 1:12). The swallow, whose Hebrew name is צִפּוֹר הַדְּרוֹר, tzippor ha-dror (literally “bird of freedom”) which must be a clean fowl, serves to symbolise the person: every person is born pure, clean of all sin, unblemished; like the swallow, the tzippor ha-dror, the bird of freedom, free to go in any direction he desires, free to choose good or evil. If he does good, he will live and receive his just reward; and if he does evil, he will be punished. And the way to achieve the good is through humility and modesty, whereas arrogance and callousness lead to denying G-d and shaking off His yoke. And this being the case, it is good for a person to be modest and humble and quiet, not to raise his voice and his head – because what is he? – Dust and ashes, decay and maggots! And what are we?! (Exodus 16:7). G-d will punish anyone who transgresses His commandments, thereby transforming his pure and beautiful and wondrous soul into something ugly. And since it is impossible to see the ugliness of a soul, G-d afflicts him with tzara’at, making him physically ugly for all to see, symbolising the ugliness of his soul (and sometimes, G-d afflicts only his garments or his house, for him to see his soul reflected therein). And he – this man who wanted to aggrandise himself above all others – is then forced to humble himself, to dwell in solitude, this man – who wanted only bodily pleasures – suffers bodily afflictions. Thus he takes two birds; one of them he slaughters, and the other one he sets free. Two birds, symbolising his free choice – good or evil.
The Abravanel comments there: The purpose here is to indicate that both the birds were previously alive – and at G-d’s command and word one of them died. Such it is with humans: one can fall sick and die, while another one remains alive. Everything depends upon G-d’s decree. And this is why He commanded [the Kohen] to slaughter the bird into earthenware vessels, alluding to the human who is as an earthenware vessel, fashioned by the hands of the Potter, blessed be He… And the bird is slaughtered over flowing water in the vessel to symbolise the Torah…because the bird who was slaughtered died because of the Torah which was not kept properly… And the Torah says that in the end “he shall send out the live bird free over the field” (Leviticus 14:7) – that is to say, to roam free in its natural habitat – symbolising that the purified person returns to the camp, there to roam free as and when he pleases, no longer to be confined. And I would add to this final detail that what this means is that he is hereby given a new opportunity for free will – if he will only learn his lesson.
Source: "Peirush HaMaccabee" on Shemot, Chapter 2, English translation by Daniel Pinner