(17) And I have said: I will bring you up out of the affliction of Egypt unto the land of the Canaanite, and the Hittite, and the Amorite, and the Perizzite, and the Hivite, and the Jebusite, unto a land flowing with milk and honey.
ואני שמעתי עוד בשם גדול אחד שאמר טעם נכון לזה כי בעת שעמדו על הר סיני וקבלו התורה [כי בעשרת הדברות נתגלה להם עי"ז כל חלקי התורה כמו שכתב רב סעדיה גאון שבעשרת הדברות כלולה כל התורה] וירדו מן ההר לביתם לא מצאו מה לאכול תיכף כ"א מאכלי חלב כי לבשר צריך הכנה רבה לשחוט בסכין בדוק כאשר צוה ה' ולנקר חוטי החלב והדם ולהדיח ולמלוח ולבשל בכלים חדשים כי הכלים שהיו להם מקודם שבישלו בהם באותו מעל"ע נאסרו להם ע"כ בחרו להם לפי שעה מאכלי חלב ואנו עושין זכר לזה:
I heard a reason for eating dairy on Shavuot, that when the Jews received the Torah they had nothing to eat besides dairy food, because meat then needed preparation, including properly sharpening a knife, exact ritual slaughter etc. Since they ate dairy, we have the custom to eat dairy on this day as well.
(7) Thou art all fair, my love; And there is no spot in thee. (8) Come with me from Lebanon, my bride, With me from Lebanon; Look from the top of Amana, From the top of Senir and Hermon, From the lions’dens, From the mountains of the leopards. (9) Thou hast ravished my heart, my sister, my bride; Thou hast ravished my heart with one of thine eyes, With one bead of thy necklace. (10) How fair is thy love, my sister, my bride! How much better is thy love than wine! And the smell of thine ointments than all manner of spices! (11) Thy lips, O my bride, drop honey— Honey and milk are under thy tongue; And the smell of thy garments is like the smell of Lebanon. (12) A garden shut up is my sister, my bride; A spring shut up, a fountain sealed.
Reason 4: The Magic Number
Rav Menachem Mendel of Ropshitz
The gematria (numerical value) of the Hebrew word for milk, chalav, is 40. We eat dairy foods on Shavuot to commemorate the 40 days that Moses spent on Mount Sinai receiving instruction in the entire Torah. Moses spent an additional 40 days on Sinai, praying for forgiveness following the Golden Calf, and then a third set of 40 days before returning with a new set of stone tablets. The numerical value of chalav, 40, has further significance in that there were 40 generations from Moses who recorded the Written Torah, till the generation of Ravina and Rav Ashi who wrote the final version of the Oral Torah, the Talmud.
Rabbi Dovid Meisels
Further, the gematria of gevina (cheese) is 70, corresponding to the "70 faces of Torah."
(ז) וּפָרָ֤ה וָדֹב֙ תִּרְעֶ֔ינָה יַחְדָּ֖ו יִרְבְּצ֣וּ יַלְדֵיהֶ֑ן וְאַרְיֵ֖ה כַּבָּקָ֥ר יֹֽאכַל־תֶּֽבֶן׃
(7) And the cow and the bear feed; Their young ones shall lie down together; And the lion shall eat straw like the ox.
Rabbi Irving Greenberg, The Jewish Way: Living the Holidays
Just as Passover evokes the future universal redemption, so Shavuot evokes the future universal covenant. The prophet predicts that even carnivorous animals will turn vegetarian [...] hence follows the anticipatory dairy meal of Shavuot.