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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 don't the last eight verses of the Torah require a minyan to read? The shiur develops a fundamental chiddush in the Rambam: Simchas Torah has two distinct takanos of Kriat HaTorah — Zot HaBracha is read from the din of Yom Tov (inyan hayom), while VaYom Moshe is read from the din of Shabbos (siyum haTorah). This explains why a new minyan is required for the last eight verses, and why the Raavad's minhag of having the oleh read (not the baal koreh) signals that the final aliyah is purely Talmud Torah, not shemiat dvar Hashem.
May a man who has already fulfilled his shofar obligation blow shofar for a woman on Rosh Hashanah? The Baal Itur forbids it while Rav Yehuda permits it. The shiur develops that the core dispute is not about violating shvus for another's benefit, but whether a man's blowing creates a "tekiah shel mitzvah" that enables the woman to be yotzei.
