What is it about milk that makes it go well with cookies?
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.