Why give a number? To explain to you that each one has to be atoned for separately, even if it was all one big "forgetting." In Elul, there is a tendency to think, "You know, let me just do a "general" Teshuvah, that should be good enough." The Talmud comes to teach us, "No, each separate action requires its own atonement, even if it was all one great forgetting."
Two kinds of Teshuvah
Niddah and Rosh Hashanah
7-day and 11-day cycles
Brachot and Rosh Hashanah
Kriat Shemah (accepting the yoke of G-d's kingship)
Shabbat and Yom Kippur
Teshuvah is a two-way process. We are knocking on G-d's door as poor people bereft of mitzvot. If both us and Hashem participate in the Teshuva process (Hashiveinu Hashem Elecha veNashuva), then both are pturim.
Eruvim and Sukkot
- Gemara discussion compares it to Sukkah.
- Aravah; mixing, shaking together the arbah minim
Pesachim and Cheshvan
Or L'Arbah Asar Bodkim et HaChametz L'Or HaNer.
Shekalim and Cheshvan
Temple, elevating the physical (two halves - male and female - see Heh and Vav
Yoma and Cheshvan/Rosh Chodesh Kislev
Yahrzeit of Matisyahu Kohen Gadol
Sukkah and Kislev/Chanukah
8 days paralleling Sukkot; siyum is the story of Miriam bat Bilgah, at the time of Chanukah, who had assimilated and married a Greek guard, who kicked the altar.
Beitzah and Kislev/Chanukah
Egg that was born on Yom Tov is something that was concealed that is now revealed
Rosh Hashanah and Chanukah/Teveth
- Rosh Chodesh was mitzvah Greeks wanted to abolish. The calendar is the source of Jewish wisdom in the eyes of the nation.
- Machloket regarding Nissan and Tishrei reflects Machloket Yehudah and Yosef
Ta'anit and Teveth/Fast of Teveth
Ta'anit is all about fasting (connection is pretty obvious). (In the division of the Mishna, it also falls here)
Megillah and Teveth
Law of Blessing before the Torah / Torah Sh'Bichtav
Moed Katan and Yud Shvat (day of Siyum)
Mourning for the Friediker Rebbe
Chagigah and Tu B'Shvat
Trees singing (Chagigah 14b)
Yevamot (and Seder Nashim) and 22nd Shvat
Yahrzeit of Rebbetzin Chaya Mushka (she was childless, although all Chabad Chassidim were her children
Ketubot and Adar/Purim
Ketubot starts by speaking about a young virgin that is to get married, like the beginning of Megilat Esther.
Nedarim and Adar
Mitzvah of Half-Shekel/obligations to the Temple needed collecting by the end of Adar
Nazir and Nissan/Pessach preparations/Omer
We don't cut our hair during the Counting of the Omer; we also take on extra stringencies related to chametz (the Nazir is told to avoid "Chometz Yayin"; we also go to the mikvah and, in order to eat the Korban Pessach, we would have to avoid contact with the dead.
Sotah and Pessach/Omer
It is customary to study the tractate of Sotah during the Counting of the Omer, as it has 49 dapim (folios) and the sacrifice brought by the Sotah was of barley, like the omer.