Cats in the movie--don't give a cat milk!

I think he was trying to downplay how much he had come to love the kitten.

When I was a kid, we had many cats on our farm, and they all drank cow's milk. On other people's farms there were even some who tried to slurp the milk directly from the udders. And no ill effects at all.
Somebody explained it to me that way: Most modern cats don't stomach milk well because their digestive system has changed after weaning. Barnyard cats drink cow's milk from the beginning and it rests their prinicipal food source for their adult lives, apart from the small animals they catch, while other pet cats start eating cat food instead.
Technically, milk is meant for young mammals — or in the case of humans: babies. But sometimes the organism does not change and the body continues to produce the necessary amounts of enzymes to digest milk.

Cats love "novelty food", whether it be milk, canned tuna, sausage…the important thing is not to give them too much of it. The "cat milk" sold by cat food manufacturers, by the way, should be fed as a treat only, too. It still contains a certain amount of lactose (same with "lactose-free" milk marketed towards humans), fat and probably some sugar, even though cats cannot taste sweet. Sugar can be found in almost all brands of cat food, it is added as a thickening agent and to make the food appear and smell better — to the human. It is a matter of dispute among cat lovers. Unlike dogs, cats are not prone to caries — but they can get fat.
But "cat milk" is a good mixer if you want to introduce young kittens to canned food. Some are a bit reluctant to eat it, but if you first give them the milk and then mix in some cat food…it usually works.