We have previously referred to the special leniency that allows a woman to remarry on the testimony of one witness. This was a most revolutionary innovation, one that seemingly violates a fundamental precept of the Torah: the basic requirement for two witnesses. Compounding the problem was the fact that the stakes were so high--adultery, illegitimate children, and the undermining of the holiness of marriage--and it is no wonder this law was not readily accepted.
Our rabbis greatly extolled the virtues of arguments for the sake of heaven. In these disputes, the disputants not only do not take their opponents' critiques personally, they welcome them; and through them, they sharpen and refine their views. Unfortunately, such disputes are rare, as most people find it difficult to separate the "person from the problem". But Beit Shammai and Beit Hillel are not most people.
"Kol Yisrael areivim zeh bazeh, all Jews are co-signers [responsible] for one another" (Shevuot 39a). This is not just a nice idea reflecting the bond we must feel for all Jews everywhere; it is a legal principle, allowing one to perform certain mitzvoth on behalf of another. It is through mitzvoth that our community is strongest.
There is arguably no greater figure in Talmudic literature than that of Hillel the Elder. He combined the Torah leadership of Moshe Rabbeinu with Aharon's peace-making and love for all. It is not by chance the Talmud teaches that if not for Hillel, Torah would have been forgotten from amongst the Jewish people (Sukkah 20a).
The Rambam, in discussing the prohibition of ba’al toseef (Devarim 4:2), the prohibition of adding to the Torah rules, said that one violates this Biblical law by claiming a rabbinic law is biblical in origin (Mamrim 2:9). The Torah gives the Sages the right and obligation to ensure the relevance of Torah to each generation by making “amendments”; gezerot, protective fences; takanot, social legislation; and rabbinic mitzvot such as the obligation to light candles on Shabbat (and Chanukah).
"A child who knows how to shake [the lulav] is obligated to take the lulav" (Sukkah 42a).
It is well known that the halacha, with rare exceptions, follows the opinion of Beit Hillel over that of Beit Shammai. What is less well known is why this is so. The Talmud notes that "a heavenly voice declared; these and those are the word of the living G-d, and the halacha follows Beit Hillel" (Eiruvin 13b).