Torah opens the soul to receive blessing

ביום השמיני עצרת תהי' לכם.

"On the eighth day there shall be an atzeres (a gathering) for you" (Bamidbar 29:35).

Shemini Atzeres is described as a day held back "for you" — for Bnei Yisrael in particular — which the Sefas Emes will explain as a special opening within their own souls.

בכל הג' רגלים נפתחו שערי ברכה מן השמים בזכות ג' אבות.

On all three Regalim (pilgrimage festivals) the gates of blessing are opened from Heaven in the merit of the three Avos.

Pesach, Shavuos, and Sukkos each draw down bracha from Above, corresponding to Avraham, Yitzchak, and Yaakov.

ושמ"ע נפתח השער בנפשות בנ"י שיכולין לקבל הברכות.

But on Shemini Atzeres the gate is opened within the very souls of Bnei Yisrael, so that they are able to receive the blessings.

The three Regalim open the gates of blessing from Above; Shemini Atzeres opens the corresponding gate below, inside the neshamos of Bnei Yisrael, making them fit vessels to receive what was sent down.

וזהו כחו של מרע"ה דכ' וידבר משה את מועדי ה' אל בני ישראל שהדביק נפשות בנ"י אל המועדות.

And this is the power of Moshe Rabbeinu, of whom it is written: "And Moshe spoke the festivals of Hashem to Bnei Yisrael" — for he attached the souls of Bnei Yisrael to the festivals.

Moshe's unique role was to bind the souls of Bnei Yisrael to the moadim, creating the inner "gate" within them through which the blessing of the festivals can be received.

והוא בכח התורה שנק' לקח טוב שמלמדת לבנ"י איך לקבל את הטוב.

And this is through the power of the Torah, which is called "a good teaching (lekach tov)," which teaches Bnei Yisrael how to receive the good.

The Torah of Moshe is the instrument that opens this inner gate; it instructs Bnei Yisrael in the art of receiving the Divine good that flows down on the festivals.

ולכן שמחים בתורה בשמיני עצרת:

Therefore we rejoice with the Torah on Shemini Atzeres.

Since it is the Torah that opens the inner gate of the soul to receive all the blessings of the festival season, Shemini Atzeres is the fitting day for Simchas Torah.

Summary: The three Regalim open the gates of blessing from Above in the merit of the Avos, but Shemini Atzeres opens the parallel gate within the souls of Bnei Yisrael, enabling them to actually receive that blessing. This is the power of Moshe Rabbeinu, who bound their souls to the moadim through the Torah — the "lekach tov" that teaches how to receive the good — which is why we celebrate Simchas Torah on this day.