Among the subjects in this week's Parsha are the laws of Kashrus. When I was in Yeshiva, one of my Roshei Yeshivas noted that from here we see that the Torah was given from Hashem. How so? Kosher animals have two signs: they both chew their cud and have split hooves. The Parsha goes on to state that only four types of animals carry only one sign – either they chew their cud or they have split hooves. At the time of Matan Torah the Jews were in a desert. They were not in the fields of Africa, nor the forests of Europe, nor the prairies of North America, nor were they in Australia; nevertheless, not one more species has been discovered as having only one sign.
On Parshas Shemini 5731/1971, the Rebbe explained a Rashi on this week's parsha. “These are the living things you are allowed to eat (Vayikra 11:2).” Moshe Rabbenu held up every animal, every bird, every fish, and all the swarming creatures and showed the Jews which is allowed and which is not. The possuk does not elaborate on this. If this is what happened, why in the parsha of Noach does the Torah take many passukim to describe how all the animals have to come two by two to the teivah to be saved from the Mabul? And here, the Torah does not go into detail and additionally, Rashi does not ask the obvious question, why does the Torah not elaborate on this great miracle? Here, all the animals, etc. came to Moshe Rabbenu in the desert of Sinai, yet this great wonder Rashi bypasses. The Rebbe answers that a child understands that Hashem wants the Bnei Yisroel to keep kosher and that the people must have a clear understanding of what is permitted and what is not permitted. Hashem brought all the animals from every continent to Moshe Rabbenu to teach the people to keep kosher. Rashi doesn't have to speak about how great the miracle was because it is self-understood.
That farbrengen in 5731(1971) was unique. Until that year, the Rebbe would farbreng on the second night of Pesach after the Seder (of course, without wine) and expound upon the Haggadah. However, the Rebbe did not conduct the Seder upstairs in the Friediker Rebbe's apartment because Rebbetzin Nechama Dina had passed away on the tenth of Teves of that year; instead he conducted his seder privately in his home. At the farbrengen of Parshas Shemini the Rebbe opened the Siddur to the Haggadah and he said a sicha explaining various parts of the Haggadah. A year later it was Shnas Hashiviim (the Rebbe's 70^th year). Beginning that year the Rebbe would farbreng on Yud Alef Nisan and various subjects about Pesach were brought up at the Yud Alef Nisan farbrengens.
The same concerning Shavuos. Until that year, after reciting Tikun Leil Shavuos the Rebbe would come down from his room to the big shul at about 3:00 AM and say a Maamar Chassidus. Since meals were no longer eaten in the Previous Rebbe's apartment, the Rebbe went home right after davenning and this late-night farbrengen ceased. Instead,beginning in Shnas Hashiviim the Rebbe would farbreng prior to every major Yom Tov, usually on the night before Yom Tov.