"Spoke the L-rd: These are the creatures that you may eat among all the animals on earth. Any animal that has a cloven hoof that is completely split into double hooves, and which brings up its cud that one you may eat.
But the pig, although it has a cloven hoof that is completely split, since it does not regurgitate its cud, it is unclean for you. You shall not eat of their flesh, and you shall not touch their carcasses; they are unclean for you."
(Levit. 11:2-4,7-8; and repeated in Deut. 14:6-8)

The Pig Says: "See, I am Pure"

...the pig...sticks out its forelegs and says "See, I am pure"...

The pig this is Edom…why is [Edom] likened to a pig?
To tell you that just as the pig, while it is wallowing in the filth, sticks out its forelegs and says "See, I am pure".
So, too, the kingdom of Aram [Edom] becomes proud and does violence and theft and [yet] appears as if it is acting justly…
The pig, this is Edom, and it does not chew its cud ["gera lo yigar"] because it does not drag after it ("goreret") another kingdom.
And why is the pig called "chazir"? Because it returns the crown to its Master, as in the verse: "The saviors will ascend to Mount Zion to judge Mount Esau [i.e. Edom] and to G‑d will be the Kingship." (Obadiah 1)

Why is it Called "Something Else"?

"We call a pig a "davar acher" ("something else") so that one shouldn’t become curious about it and come to eat it, just as we don’t mention the name of bread on Pesach for this reason." A great Sage in Midrash Tanchuma is quoted by Rabbeinu Bachayei in Parashat Shemini – "Why is the pig called "chazir"?
Because in the future the law about [its permissibility] will return [to the way it was before]."

There is a version that reads: "in the future the crown will return to as it was in the old times" and another version reads "in the future it will return to us". The common people understand that in the future the pig will be permitted, but greater insight into the matter is that the [evil] inclination in Israel will lend assistance to us afterwards and will increase peace, as is said, "The wolf will lie with the lamb".

Heaven forefend that this implies that the Torah of G‑d which we accepted at Sinai will change, for it will never be exchanged and He will never abandon His Law, tec. The commentators have already explained this at length. What is meant by the verse, "there will not be any survivor" is that the impure will be toppled and the holy will remain…

The common people have become accustomed to say that the pig will in the Future return to us and be permitted, and there are those who have a craving for its meat because it is fat and rich, and there are those of small intellect who, based on the name ("chazir"), will demand that pig be permitted, saying "why should we wait, permit it to us immediately". For this reason it is referred to as "davar acher".

[Sefer Hamagid]

The Pig Will Chew its Cud in the Time to Come

But in the Time to Come, [the pig] will chew its cud and will return to being permitted.

"The pig…but it does not chew its cud." This explanation is actually a condition, meaning "as long as it doesn’t chew its cud". But in the Time to Come it will chew its cud and will return to being permitted. It will not remain in a condition where it does not chew its cud, rather it [will change its nature and chew its cud and therefore it] will be permitted, but the [law of the] Torah does not change.

[Ohr Hachaim]

The Pig is Like the Tree of Knowledge

In the time to Come the Holy One, blessed be He, will announce "Anyone who didn’t eat pig’s flesh may come and collect his reward." It is difficult – why announce about a negative mitzvah of eating, any more than the rest of the negative mitzvahs of other forbidden activities which do not pertain to eating. Further, why make such an announcement about pig, and not about the rest of the impure animals and torn animals [which are also forbidden to eat]?

According to what is said about the Yetzer Hara, that it is made from the power of the pollution of the primordial snake, who caused Adam and Eve to sin and this is the reason why it is fitting to blame him for all the sins. And in particularly the sins of forbidden eating, for the sin of Adam and Eve – from which was drawn the pollution of the snake, from which the lowly Yetzer Hara comes – it was the sin of eating from the Tree of Knowledge. But this was [the Tree of Knowledge of] good and evil, as stated in the verse, and the good was revealed, as it states: "and the woman saw that the tree was good for eating", that the good was revealed in it and she saw it, but the evil was submerged within it like the venom of a snake which is hidden within it and is not seen from the outside.

The pig is similar to the tree which, contained good and evil, for it possesses a sign of purity which is revealed and visible from the outside – it has split hooves, which is visible to all. But it has a sign of impurity in that it does not chew its cud, and this sign of impurity is hidden and not openly seen. Thus it is explicitly stated in the verse, "the pig, because it has split hooves and does not chew its cud, is impure to you."

...the pig is of a similar nature to the tree from which Adam ate, which contained good and evil...

We find that the pig is of a similar nature to the tree from which Adam ate, which contained good and evil and the good was revealed and the evil was hidden, as was stated. Therefore, our Sages have said: "Why is the pig called "chazir"? Because in the Future it will return to be permitted – after the Tree of Knowledge of Good and Evil will be rectified; and since the pig is of a similar nature, then it, too, will rectified and will become completely permitted."

According to this, since the pig is of a similar nature to the Tree of [Knowledge of] Good and Evil, then the one who is careful to keep away from [eating] pig flesh cause the rectification of the Sin of [the Tree of] Knowledge more through keeping this mitzvah than keeping all the other mitzvahs. Because the pig is truly of a similar nature to the tree that Adam ate from, which is good and evil, and he [the one who keeps this mitzvah] breaks and humbles this yetzer Hara, which comes from the pollution of the snake, more than the rest of the mitzvahs. For this reason will the Holy One, blessed be He, make an announcement about the keeping of this mitzvah, more than keeping [the mitzvahs to refrain from eating] the other impure beasts, and more than other negative mitzvahs which do not pertain to eating.

[Ben Ish Chai, Derush 3 L’Shabbos Teshuva]

Kelipat Noga, enjoying Physical Pleasures

...it is KelipatNoga which turns its face and its inner aspect (penimiyut) to physical desires...

The food of the pig is excrement, which is the waste of what was refined from [the food eaten by] the person, as it says regarding Pe’or [the idolatrous worship of Ba’al Pe’or] that they would defecate [in front of this idol as a means of worship] in order to receive from the waste, which is physical pleasures. Also…the verse "ki panu alai oref/because they turned the back of their neck to me" is translated as "they returned (machazrin) to me the back of the neck", which is the matterof pig ("chazir") for it is Kelipat Noga which turns its face and its inner aspect (penimiyut) to physical desires, and only the back of its neck is turned to holiness, and it says about Judah: "you will grasp your enemies by the back of the neck", for he killed Esau who is called pig, as in the verse in Psalms: "all the goyim 'mechazrin'/surrounding me".

The matter of returning the crown, from which is drawn the contemplation as to: "if those who violate His will [receive such splendid beneficence from Above]…" that in the waste and excrement there is so much pleasure, "…then those who keep His will, how much more so," and this is the additional light that comes from the darkness…and the crown is Malchut; "and the saviors ascended to Mount Zion to judge the Mountain of Esau" then "there will be to G‑d the kingship", which is "if they do teshuva they are redeemed" because teshuva means to return to be face to face, the opposite of the aspect of the pig, for [via teshuva] he returns his face, etc. and then "you will grasp your enemies by the back of the neck"…

[Ohr Hatorah of the Tzemach Tzedek, parashat Vayikra I, p. 48]

The Pig Returns, This is Esau

It says in the midrashim of our Sages that the 4 Kingdoms [in which Israel is exiled] (Bavel, Yavan (Greece), Madai, and Edom [Rome]) are likened to the 4 animals which are mentioned explicitly in the verse that forbids eating them because they only possess one sign of purity.

 

In this itself there are 2 parts:
1) "the camel and the hare and the badger, because they chew their cud but they do not have split hooves;
2) "the pig because it possesses split hooves but does not chew its cud".

The camel and the hare and the badger refer to Bavel, Yavan, and Madai, and the pig refers to Edom [Rome], as in: "the pigs of the forest ravage it" (Psalms 80:14) — "just as a pig at the time he wallows [in the filth] sticks out his forelegs and says ‘look, I am pure’, so, too, the kingdom of Edom…" (Vayikra Raba 13) For this reason it is mentioned separately [as explained by Rabbeinu Bachaye] "in order to show that it [the fourth exile, the exile of Edom] is a lengthy exile in and of itself and is equal to all the others."

Via "our actions and our avoda" in the exile of Edom do we bring about the refinement of Edom...

Via "our actions and our avoda" in the exile of Edom do we bring about the refinement of Edom, as our Sages say, "in the future the pig will become pure" (for at that time it will possess both signs [of being pure] – split hooves and raising the cud), as the closing words of the Midrash "the pig this is Edom, which does not chew its cud and is not followed by any kingdom after it". Why is the pig called "chazir", for it returns the crown to its master, as we say: "the saviors ascended to Mount Zion to judge Mount Esau and to G‑d will be the Kingship", for then will be fulfilled the promise to Yaakov: "until I come to my master in Se'ir" [upon which Rashi comments] "when will he go – in the days of Moshiach, as it says ‘the saviors shall ascend to Mount Zion to judge Mount Esau’. (Gen. 33:14)

[Lubavitcher Rebbe, Hisva'aduyot 5750 I, p. 351]

[Excerpted from "Yalkut Moshiach U’Geulah al HaTorah" by Rabbi Dovid Dubov of Princeton, translated by Rabbi Yaakov Bock of New Jersey, first published in Chayenu.]