Why Are Eggs Kosher?
Gemara Chullin 64a
Chizkiyah explains (Chulin 64b) that eggs of a non-Kosher bird are also not Kosher since the Torah lists amongst the non-Kosher species, the bird and its baby, "VeEs Bas HaYaAnah" (Vayikra 11:16) thereby teaching that the egg is also not Kosher.
But there is a problem - the Torah has already taught this. "Kol HaYotzei Min HaTamei - Tamei" - whatever emerges from a non-Kosher animal is also not Kosher; for example, ostrich eggs and camel milk (Bechoros 6b)
Tosafos (DH ShaIm Rikmah VeAchlah) explains that this problem has already been encountered and resolved in the Gemara (Bechoros 6b) regarding cow milk. The Gemara posits that milk of all beasts - even Kosher beasts - ought to be prohibited under the rubric of the limb which is separated whilst the beast still lives and milk is taken from the beast whilst it lives. The Gemara explains that the Torah provides a special exemption to permit milk. Which brings us back to our problem with eggs being Kosher because they too come from a living beast and ought not to be Kosher.
Milk has a special exemption, but do eggs have a special exemption? No. In that case all eggs ought to be non-Kosher.
There is however a very strange twist to this analysis. When the Torah grants permission to drink cow's milk, by exempting it from being a "limb from a living beast", the Torah might mean that milk is not deemed to be part of the beast at all, in which case even milk of a camel for example,will be Kosher.
And that my friends, is how the Gemara (Bechoros 6b) explains why the Torah must tell us that camel milk is not Kosher; we would otherwise have Paskened that it is not a part of the camel at all and is Kosher.
Tosafos proceed along the same lines to explain why eggs are Kosher: they have a special exemption alluded to in the Mitzvah of not taking the eggs or fledglings whilst the mother is nearby (Chulin 140). Again, we would understand that the Torah is teaching us that the eggs are an independent entity and unrelated to the birds laying them, meaning that ALL eggs, even ostrich eggs, are Kosher.
And that my friends, is why the Gemara (Chulin 64b) explains why the Torah must tell us that eggs from non-Kosher birds are not Kosher. We would otherwise have Paskened that eggs are not at all associated with the bird that lays them but are an independent entity and are Kosher.
The only discomfort is that the Gemara says this only about milk and it is Tosafos who present this identical argument for eggs; why did the Gemara not put them all [their eggs] in the one basket and deliver one answer to address both issues?
The Mishnah (Bechoros 5b) states that everything that emerges from non-Kosher animals is not Kosher, by Torah Law.
Yet the Gemara (Chulin 99b) explains that fluids from non-Kosher fish are actually Kosher and only prohibited by Rabbinic decree.
The KEHILOS YAKOV (Avodah Zarah 20:2) explains: there are two categories of non-Kosher. Some non-Kosher species are identified with the phrase, "HaTemeIm" (e.g. Vayikra 11:7; see also ROSH to Avodah Zarah 2:42). Kosher animals not fit as a Korban (Vayikra 27:11; see Rashi there) and Kosher animals that became Tereifah are also so identified.
It is only the fluids from these beasts that is not Kosher.
However, the Torah does not identify non-Kosher fish as "Tamei", rather they are "Sheketz" (Vayikra 11:10) and the fluids emerging from them is Kosher according to Torah Law. (The Kehilos Yakov points out that his approach is not consistent with the words of Tosfos in Chulin 99b.)
The CHAVOS DA'AS (YD 81:1) without explaining why simply posits that this rule does not apply to non-Kosher fish. It is simply a fact, the brine of fish is "ZeiAh BeAlma", it is a waste product, not food and cannot be defined as non-Kosher. (Chulin 99b)
The Isur of Ever Min ha'Chai should prohibit Nochrim from drinking milk, since the verses that permit milk apply only to Jews. Why is a Nochri permitted to consume milk products?
(a) The TESHUVOS CHASAM SOFER (YD 19) concludes that the allowance for Nochrim to consume milk products may be derived from the conduct of Avraham Avinu, who served milk and butter to his guests (Bereishis 18:8) who, he thought, were Nochrim. Avraham Avinu certainly would not have served such foods to Nochrim had they been forbidden to eat them.
Similarly, the SHITAH MEKUBETZES (#2) writes that Avraham Avinu's conduct cannot prove that milk is permitted to Jews, because Avraham fed the milk products to Nochrim (or at least to whom he thought were Nochrim). Even though Nochrim have a prohibition of Ever Min ha'Chai, they never accepted upon themselves a prohibition against eating milk, as they did the other Mitzvos of Bnei Noach (Bava Kama 38a).
However, TOSFOS in Chulin (64a) points out that eggs also come from a live animal, and thus a special verse is needed to permit them. The verse that permits eggs is the verse that teaches the Mitzvah of Shilu'ach ha'Ken (Devarim 22:7). Since the Torah commands a person to send away the mother bird from the nest before he takes the eggs, it clearly permits the consumption of eggs. However, this verse only permits eggs to Jews, but not to Nochrim, who have no Mitzvah of Shilu'ach ha'Ken. The Chasam Sofer's source for the Heter for Nochrim to drink milk does not include a Heter for them to eat eggs, since Avraham Avinu did not serve eggs to his guests. What is the source to permit Nochrim to eat eggs?
(b) TOSFOS in Chulin (33a, DH Echad) and others rule that it is not possible that something should be permitted to a Jew and forbidden to a Nochri. Accordingly, eggs -- which are permitted to a Jew -- must be permitted to a Nochri as well. The same applies to milk. (This does not apply to eggs or milk from a Tereifah animal. According to Tosfos, since a Jew may not eat eggs or milk from a Tereifah animal, they should also be prohibited to a Nochri, since there is no source to permit them.)
However, the RAMBAM (Hilchos Melachim 9:13) rules that it is possible for something to be permitted to a Jew and forbidden to a Nochri. Accordingly, Nochrim should not be allowed to eat eggs.
The Chasam Sofer concludes that according to the Rambam a Nochri may not eat eggs, and a Jew may not offer him eggs because of "Lifnei Iver." According to Tosfos, one may not offer Tereifah eggs to a Nochri to eat.
However, one may sell eggs to a Nochri without specifying that they are for eating, because the Nochri might intend to use them for a purpose other than eating. Moreover, since it is easy for the Nochri to find eggs, a Jew does not transgress "Lifnei Iver" by giving them to a Nochri.
HALACHAH: Many Acharonim point out that it is not necessary to prove that milk and eggs are permitted to Nochrim. The KEREISI U'PLEISI (YD 81) writes that although something that comes from a live animal is prohibited, it is not prohibited because of the Isur of Ever Min ha'Chai. Rather, the prohibition is derived from a second verse that teaches that anything produced by a forbidden object is forbidden like the object itself. That second verse addresses only Jews, and not Nochrim. Accordingly, a source to permit milk and eggs is necessary only to permit them for Jews. For Nochrim, there is no reason to prohibit them in the first place, because they are not included in the prohibition of Ever Min ha'Chai.
The REISHIS BIKURIM finds support for this reasoning in the words of the Shitah Mekubetzes (#2), who writes that a Nochri would be allowed to drink milk even if milk had not been permitted to Jews, since the prohibition of milk is not included in any of the seven Mitzvos of Bnei Noach.