I don't drink milk myself, but among my friends that do, the one application where they find soymilk a poor substitute is the classic dish "milk and cookies". What is it about cow's milk that makes it go well with fresh-baked cookies that soymilk cannot replicate? It can't be the fat content alone, because my roommate drinks exclusively fat-free skim milk.
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I haven't been able to find any empirical data, but here are my theories:
Most cookies contain butter which has similar proteins as milk and the combination of the two resonates on that level. Soy milk does not share those protein profiles, so there is no sensory resonance.
Cookies are generally quite sweet and rich. Milk helps blunt that sweetness by washing away some of the sugar and coating the tongue. Many soy milks have sweeter taste than dairy milk which would make the overall sweetness of the combination excessive. (For comparison's sake does your roommate use soy milk on sweetened cereals or more neutral-tasting cereals? I would suspect the latter.)
In addition to the natural "grassy" flavors that soy milks can have, they may also have other flavorants like vanilla that make them less neutral flavored than dairy milk which competes with the flavor of the cookies.
The fat, protein, calcium, water in the milk make the snack more nutritious and healthy without changing into another taste experience like, say, cookies and salad. Like the cookie, milk is still a sweet taste (lactose) and a rich experience (calories and fat). Combined they make a great snack or desert experience. It seems evolutionary to me that we would favor a food that not only gives us quick energy (simple sugars in cookies) but also necessary molecules of protein, fat, water. If you were to combine the cookie with a different nutritional food, you are no longer enjoying the indulgence of a rich, sweet dessert, and changing the experience to an odd one. Also, cookies are dry, so liquid calories are a nice compliment.