I was wondering whether the product of an animal should be defined as animal, and I decided no on the grounds that anything man-made would therefore by extension also be animal.

Butter? Lamb Chop? Surely anything 'man-made' should be classified by its material composition?

Absolutely - hence why it would be inconsistent to describe milk as animal because it's made of minerals but produced by a cow, but a CD mineral cos it's made of plastic and produced by a human.

Now your tending towards syllogism :-) We're arguing on two fronts here - firstly 'What is milk'? which we disagree on; secondly 'anything man-made should be classified by its material composition' which we agree on. I don't see the logical step from one to the other. Perhaps I'm a bit tired.

[Chalky] If milk, an animal by-product, is 'animal', what about dung? By your argument it's 'animal', but surely it's 'vegetable', since that's what the cow ate. Or possibly 'mineral', if you figure it's been broken down that far.