I believe dairy also contains cheese. Dairy food group contains milk, cheese, yogurt, milk-based desserts, and soy-milk. That's a bit different than the meat/protein group.
See here
What Is Dairy? - Food Groups - ChooseMyPlate.gov - USDA
"All foods made from meat, poultry, seafood, beans and peas, eggs, processed soy products, nuts, and seeds are considered part of the Protein Foods Group. Beans and peas are also part of the Vegetable Group."
The above paragraph is from that site. I agree it's very confusing.