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Why couldn't Korban Pesach (פסח) be missed, requiring Torah (תורה) to create Pesach Sheni for those unable to bring it? The korban represents our fundamental commitment to bris with Hashem (ה׳) and separation from avodah zarah. It transforms us into a tzibbur united by covenant, making participation essential for membership in Am Yisrael.
Korban Pesach (פסח) represents our committing ourselves to bris with Hashem (ה׳). It showed our separation from a"z - "Mishchu u'k'chu" - along lines of Luchos - which were acceptance of entire Torah (תורה). Thus, the KP couldn't be missed - and Torah allowed make-up of Pesach Sheni. We're also careful to convey its message to all of Israel: we communicate it to each of arba banim (of Haggadah) in manner he'll best relate to. The KP is a korban tsibbur in that it makes us into a tsibbur.
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Why doesn't Chanukah appear in the Mishna? The shiur develops a fundamental yesod: Chanukah represents the victory of Gemara—the human ability to use godly intellect (ner Hashem nishmas adam) to develop Torah SheBaal Peh. The Menorah symbolizes the soul's illumination through this koach, while the Mizbeach represents the body's recreation—together forming the complete tikkun of man.
Why does Megillas Esther interrupt Torah study for a message the world deemed ridiculous—that every man should rule his home? The shiur develops the yesod that the moon's willingness to "make itself small" doesn't diminish it but creates unified sovereignty. A woman who enables her husband to lead isn't relegated to second class—she is the king-maker, comfortable creating oneness where a man cannot.