Shemini Atzeres/Simchas Torah
We experienced Sukkos with all its special mitzvos. Now comes Shemini Atzeres, which has no unique mitzvah. This is unusual. Pesach has matzah, Rosh Hashanah has shofar, Yom Kippur has fasting, Sukkos has sukkah and lulav. Shemini Atzeres has none.
When Sukkos comes to an end, Hashem says to us, “Kasheh alai p’reidas’chem – I don’t want you to leave.” Hashem knows that when the holidays are over, we are liable to leave Him and drift away because we lack special mitzvos to keep us attached. This may be compared to someone hooked up to a respirator. When he is disconnected, he doesn’t have the ability to breath on his own. So it is when the holidays are over. We are liable to leave Hashem and drift away.
That’s why we have Shemini Atzeres. No sukkah, no lulav. It is a Yom Tov on which we rejoice with Hashem without any external help. This is the avodah of Shemini Atzeres: to be close and attached to Hashem without any practical mitzvos to fulfill. This gives us the strength to continue that way all year long!