Shavuot is not a dairy holiday
This holiday’s name in the Torah is “festival of first fruits” or “festival of harvest” and it indicates the obligation of bringing a plant sacrifice to the temple from the first fruits of your land (The choice first fruits of your soil you shall bring to the house of the Lord your God). Those first fruits are of the Seven Species which were first to ripen. Others say that the mitzvah is to bring a sacrifice of “two breads” since those would be the first sacrifice made from the new wheat (in both cases it is a plant sacrifice). The name “Shavuot” is based on the counting of 7 weeks between Passover and Shavuot. So how did we get from that to celebrating with dairy products?
Customs. It is important to clarify that customs are not halacha and there’s no obligation to uphold them. In the past there used to be a custom of decorating synagogues with trees which the Gra cancelled because other nations were doing the same thing on their holiday.
This is the nature of a custom, it comes and goes based on the time, place and instruction. We know there are different customs between the different Ashkenazi and Sephardi communities. For example, Yemenite Jews did not use to eat dairy products on Shavuot at all. The custom comes from Ashkenazi and French Jews in the 14th century.
Another reason for this custom is that at the time the Jews got the Kashrut laws their dishes were unusable so they resorted to eating dairy until they kashered their dishes. There are tens of other reasons but the connecting link between all of them is that you should not follow a custom which breaks halacha. At the time this custom came to be, there was no animal industry, people had cows in their yard and they would take some milk while the calf would still suckle. In our days, when dairy products are coming through serious sins and are the product of tzaar baalei chaim, the enjoyment of eating it is enjoyment coming from a sin. It is also forbidden to buy it due to “assisting a person who’s making a sin.” Therefore, it should not be put on the holiday table and with today’s abundance. Milk products are easy enough to replace with natural, sweet and tasty foods.
Why was Israel named a land flowing with milk and honey?
A land flowing with milk and honey. Rabbi Eliezer says: milk – is the fruit milk, honey – is date honey. (מכילתא דרשב”י יג) “Just as You have sworn to our forefathers, a land flowing with milk and honey, so that You will give taste to the fruit.” (רבינו בחיי, דברים כו)
“A land of fruits rich as milk and sweet as honey.” (יהונתן בן עוזיאל, דברים ו, ג) “A land of milk and honey meaning a land rich and prosperous with all its fruits.” (עקידת יצחק, דברים שער פט) “For God said ‘a land of milk and honey’ which is a land that has ripe and sweet fruits.” (אלשיך דברים ו)
Israel was blessed with the seven species and only those were brought to the temple. Milk and bee honey are not included in these. “For the Lord your God is bringing you into a good land, a land with streams and springs and fountains issuing from plain and hill; a land of wheat and barley, of vines, figs, and pomegranates, a land of olive trees and honey;” (this is date honey)
When the spies who are returned from scouting Israel they describe how good it is; “it does indeed flow with milk and honey, and this is its fruit” and they brought with them samples of the fruit, not milk.
Even according to those who believe that milk is the milk of goats, it is talking about excessive milk that drops on its own as Rashi says “it comes out without touching.” (מגילה ו, א) Milk, as a product of pregnancy is a symbol of fertility and abundance.
On Shavuot we can celebrate the sweetness of Torah with date honey and other tasty foods.