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).
One of the most difficult things for we humans to do is to admit that we are wrong. Even when we know we have acted in ways that leave much to be desired, we are great at offering excuses, rationalizations, justifications, and the like. This is especially so when we are dealing with an act of omission, rather than one of commission. There are always good reasons to explain why we did not do something.
“And Moshe was one hundred and twenty years when he died” (Devarim 34:7). It is a beautiful, if somewhat unrealistic, custom to offer blessings to those celebrating a birthday that they should live to be 120. While this quantity of life is (usually) unrealistic, the blessing to live to 120 relates not only to quantity, but to the quality of life; “his eyesight did not diminish and his strength did not wane” (ibid).
One of the underlying pillars of democratic thought is confidence in the people to make the right choices, and in leaders to respect those choices. In a healthy democracy, people are well informed, allowing for vigorous debate; and leaders have the best interests of the state at heart. The will of the people is constricted by the Constitution, which reflects the core values that are sacrosanct—and as such, can be changed only with great difficulty and a consensus to do so.
While Korbanot tzibbur, public offerings, were sacrificed on Shabbat and Yom Tov--and serve as the basis for our davening mussaf on these days--private sacrifices were not.
Similar to a public offering, the korban pesach was brought at a fixed time. On the other hand, the obligation to bring such rests on the individual, leading to uncertainty as to whether it may be brought on Shabbat.
One of the most famous Talmudic stories is that of the potential convert who conditioned his conversion on whether or not he could be taught the Torah while standing on one foot. Shammai, bothered by the chutzpah of this non-Jew (imagine going to a nuclear physicist and asking to learn all of physics while standing on one foot!), “pushed him with the construction board in his hand”. Hillel, non-plussed by this ludicrous request, simply answered, “What is hateful to you, do not do to others; all the rest is commentary. Go and learn”.