Your question seems to imply that beef is a really common ingredient in Chinese food. It isn't. Beef is - or at least up until extremely recently was - really rare in Chinese cuisine (to wit, I defy you to find me a beef-based dumpling in Mainland China). And the reason for this is straightforward enough: oxen are far more valuable for their labor-capacity than for their meat... and by the time they're worn out, what meat is left is virtually inedible. There was never any real market for the product... up until, that is, the proliferation of Western dietary patterns in the late 20th century.

Instead, the Chinese diet has consisted - in terms of animal protein - around pork, chicken, duck, fish, and (in the north and west primarily) goat. To this day, you really don't find many beef dishes in what you'd consider "traditional" Chinese cuisine. This is because, again, it would have been an irresponsible use of a resource.

Thus bovines never gained the reputation as being a "food" animal like swine or fowl. That, combined with the markedly higher-that-European-incidence of acute lactose intolerance, and there was never any reason to adopt a milk-based culture.

Contrast that, however, with China's immediate neighbors, and you see that it is not some "Asian" thing in general - Mongols to the north and Tibetans to the west based their traditional diets on horse and yak milk and flesh, respectively. Presumably, as with Europeans, those individuals across time who could not physically handle such a diet were... selected against ... whereas the Han Chinese in general were not, owing in large part to a much broader range of food options.