The Gemara establishes that Shavuot is uniquely the festival given for the sake of Torah, and all opinions agree one must rejoice with eating and drinking on Shavuot. The counting from Rosh Chodesh Sivan gives context to why this period is one of joyful anticipation.
(עב״ם סִימָן) אָמַר רַבִּי אֶלְעָזָר: הַכֹּל מוֹדִים בַּעֲצֶרֶת דְּבָעֵינַן נָמֵי לָכֶם. מַאי טַעְמָא? יוֹם שֶׁנִּיתְּנָה בּוֹ תּוֹרָה הוּא. אָמַר רַבָּה: הַכֹּל מוֹדִים בְּשַׁבָּת דְּבָעֵינַן נָמֵי לָכֶם. מַאי טַעְמָא? ״וְקָרָאתָ לַשַּׁבָּת עוֹנֶג״. אָמַר רַב יוֹסֵף: הַכֹּל מוֹדִים בְּפוּרִים דְּבָעֵינַן נָמֵי לָכֶם. מַאי טַעְמָא? ״יְמֵי מִשְׁתֶּה וְשִׂמְחָה״ כְּתִיב בֵּיהּ. מָר בְּרֵיהּ דְּרָבִינָא כּוּלַּהּ שַׁתָּא הֲוָה יָתֵיב בְּתַעֲנִיתָא, לְבַר מֵעֲצַרְתָּא, וּפוּרְיָא, וּמַעֲלֵי יוֹמָא דְכִיפּוּרֵי. עֲצֶרֶת — יוֹם שֶׁנִּיתְּנָה בּוֹ תּוֹרָה. פּוּרְיָא — ״יְמֵי מִשְׁתֶּה וְשִׂמְחָה״ כְּתִיב. מַעֲלֵי יוֹמָא דְכִיפּוּרֵי — דְּתָנֵי חִיָּיא בַּר רַב מִדִּפְתִּי: ״וְעִנִּיתֶם אֶת נַפְשׁוֹתֵיכֶם בְּתִשְׁעָה לַחֹדֶשׁ״, וְכִי בְּתִשְׁעָה (הֵם) מִתְעַנִּין? וַהֲלֹא בַּעֲשִׂירִי מִתְעַנִּין! אֶלָּא לוֹמַר לְךָ: כׇּל הָאוֹכֵל וְשׁוֹתֶה בְּתִשְׁעָה בּוֹ — מַעֲלֶה עָלָיו הַכָּתוּב כְּאִילּוּ מִתְעַנֶּה תְּשִׁיעִי וַעֲשִׂירִי. רַב יוֹסֵף בְּיוֹמָא דַעֲצַרְתָּא אָמַר: עָבְדִי לִי עִגְלָא תִּלְתָּא. אָמַר, אִי לָא הַאי יוֹמָא דְּקָא גָרֵים — כַּמָּה יוֹסֵף אִיכָּא בְּשׁוּקָא.
Ayin, beit, mem is a mnemonic consisting of the first letter of Atzeret, the middle letter of Shabbat and the final letter of Purim. Rabbi Elazar said: All agree with regard to Atzeret, the holiday of Shavuot, that we require that it be also “for you,” meaning that it is a mitzva to eat, drink, and rejoice on that day. What is the reason? It is the day on which the Torah was given, and one must celebrate the fact that the Torah was given to the Jewish people. Rabba said: All agree with regard to Shabbat that we require that it be also “for you.” What is the reason? Because the verse states: “If you proclaim Shabbat a delight, the sacred day of God honored” (Isaiah 58:13). Rav Yosef said: All agree with regard to Purim that we require that it be also “for you.” What is the reason? Because it is written: “To observe them as days of feasting and gladness” (Esther 9:22). The Gemara relates: Mar, son of Ravina, would spend the entire year fasting during the day and eating only sparsely at night, except for Shavuot, Purim, and the eve of Yom Kippur. He made these exceptions for the following reasons: Shavuot because it is the day on which the Torah was given and there is a mitzva to demonstrate one’s joy on that day; Purim because “days of feasting and gladness” is written about it; the eve of Yom Kippur, as Ḥiyya bar Rav of Difti taught: “And you shall afflict your souls on the ninth day of the month in the evening, from evening to evening you shall keep your Sabbath” (Leviticus 23:32). But does one fast on the ninth of Tishrei? Doesn’t one fast on the tenth of Tishrei? Rather, this comes to tell you: One who eats and drinks on the ninth, the verse ascribes him credit as if he fasted on both the ninth and the tenth of Tishrei. The Gemara relates that Rav Yosef, on the day of Shavuot, would say: Prepare me a choice third-born calf. He said: If not for this day on which the Torah was given that caused the Jewish people to have the Torah, how many Yosefs would there be in the market? It is only due to the importance of Torah study that I have become a leader of the Jewish people, and I therefore have a special obligation to rejoice on this day.