The Torah belongs to Bnei Yisrael below

איתא בגמ' הכל מודים בעצרת דבעינן נמי לכם יום שניתנה בו תורה לישראל הוא.

It is stated in the Gemara: all agree that on Atzeres (Shavuos) we require also "for you" (a portion of physical enjoyment), since it is the day on which the Torah was given to Yisrael (Pesachim 68b).

Even the Tanna who generally holds a Yom Tov can be devoted entirely to Hashem concedes that Shavuos must include "lachem" — a share of bodily celebration — because it commemorates Matan Torah, which was given specifically to Bnei Yisrael in this world.

דבודאי כל המחלוקת דתנאים ואמוראים המה נמי בשמים כדאיתא אלו ואלו דברי אלקים חיים.

For certainly all the disputes of the Tannaim and Amoraim exist in Heaven as well, as it is stated: "These and those are the words of the living God" (Eruvin 13b).

The Sefas Emes lays the groundwork: machlokes is not merely a human disagreement. Both sides reflect genuine spiritual realities Above — "eilu va'eilu" — so each opinion corresponds to a real mode of Divine conduct.

פי' שיש כמה מיני הנהגות למעלה ויש עולמות ומלאכים שתלוין במעשה התחתונים וכפי הנהגה זו מתקיים השיטה חציו לה' וחציו לכם.

The explanation is that there are several modes of conduct Above: there are worlds and angels that depend upon the deeds of those below, and according to this mode of conduct the view "half for Hashem and half for you" is upheld.

One whole order of the upper worlds is sustained by human avodah. With respect to that order, the Yom Tov must be split — "half for Hashem and half for you" — because man's physical involvement actually feeds those worlds.

ויש עולמות ומלאכים שאין תלוין במעשה התחתונים וכפי הנהגה זו מתקיים השיטה כולו לה' כו'.

And there are worlds and angels that do not depend upon the deeds of those below, and according to this mode of conduct the view "entirely for Hashem" is upheld.

There is another order of upper worlds that needs nothing from human action. Relative to that order, the Yom Tov can indeed be "kulo laHashem" — wholly devoted to Hashem — since no "lachem" portion is required to sustain it.

אבל בעצרת שניתן בו התורה ואיתא הכל נעשין אוהבין למרע"ה ומסרו לו מתנות.

But on Atzeres, when the Torah was given — and it is stated that all (the angels) became lovers of Moshe Rabbeinu and handed over gifts to him (Shabbos 88b–89a).

At Matan Torah the very angels who had at first objected to giving the Torah to mortals were won over; they befriended Moshe Rabbeinu and gave him gifts. Their change of heart is the key to the sugya.

הגם דאותן שקטרגו מקודם א"כ הם מאלה המדריגות שאינם צריכין למעשה התחתונים.

Now, those angels who had earlier objected — they belong, then, to those levels that do not need the deeds of those below.

The angels who first protested were precisely from the higher order that is self-sufficient and does not depend on human deeds — which is exactly why they saw no reason the Torah should be entrusted to people of flesh and blood.

אעפ"כ הודו שהתורה צריכה אל בנ"י וז"ש הכל מודים בעצרת כו':

Nevertheless they conceded that the Torah needs Bnei Yisrael — and this is the meaning of "all agree on Atzeres."

Even those self-sufficient angels admitted at Matan Torah that the Torah belongs in the hands of Bnei Yisrael down here. "All agree on Atzeres" thus means more than a halachic point: even the highest, independent levels concede that this day, and the Torah itself, require the physical "lachem" of Yisrael.

Summary: Building on "eilu va'eilu," the Sefas Emes explains that some upper worlds depend on human deeds (hence "half for Hashem, half for you") and others do not (hence "wholly for Hashem"). At Matan Torah even the loftiest, self-sufficient angels — who had first objected to giving Torah to mortals — conceded that the Torah needs Bnei Yisrael in this world. That universal concession is why "all agree" that Shavuos must also be "for you."