The upper class spoke French and when they asked for beouf, they wanted meat, not a cow. Likewise when they asked for poulet, they wanted a cooked chicken, not a live one.
The lower classes spoke German and gave us cū (kuh in modern German) for a cow and cīceb (Küchlein in modern German) for chicken.
As English grew from both of these roots, the different words remained.
Nevertheless, s0rce is correct on the original linguistic point: that the Norman food-word is "mutton", whereas "lamb" is the Germanic word for the young animal.
Captain Pedantic, checking in: it should be "sheep/mutton" and "lamb/lamb". Lambs are baby sheeps.
But that's another time and another place; I'm kind of curious about when the change came about. Partly because, were that article written thirty years ago I would have argued that it is wrong. But I've since become a vegetarian, and might not have gotten the memo when the change came about. Or maybe I've always been wrong, along with all the other hicks I grew up with. :-)
At this point you might be right, but the origin is about wanting to fit in with the new french overlords.
In regular language, you would call porc the meat that comes from a cochon, and bœuf the meat of a vache.
It's not as clear cut as in English, as a bœuf is also an ox, and you can also call a pig a porc, but I think it indicates that the linguistic distinction between an animal and its meat is indeed at its core a dehumanizing process, it might just have been helped by the French-speaking rulers of England, but it still happened in France eventually, more recently and without exterior intervention.
Why? I feel absolutely no emotional difference between "cow meat" and "beef", and would be surprised to hear that it really made a difference to pretty much any non-vegetarian... Further, it seems nobody has felt the need to introduce a different word for 'lamb' - it's still an extremely popular meat despite the word literally meaning 'baby sheep'...
I think it's drawing a really long bow to think it's desensitising language (dehumanisation isn't really the right word, since cows, sheep etc. aren't human). At the end of the day, I think it's just a quirk of language development...