It’s a fucking bottle of milk, it’s not insulin. You’re doing the kid a favor by refusing.

Kind of surprised by some of the responses here.

The kid doesn't need the milk, but there's basically no upside to refusing:

Any adult that hears your response (or learns about it later) is going to come away with a very negative perception of vegans.
This may apply to the kid (maybe later on), or at the least they'll just be confused and think you're mean.
The kid is already holding the bottle of milk, whatever harm the demand caused is already done. If the kid throws the milk away and buys some other beverage, that's probably going to be more harm overall: basically anything we eat causes some amount of animal suffering, human suffering, environmental damage, etc.

Would you cook a hamburger for the kid if he looked up at you with big eyes and said pweeeze?

There's a massive difference between opening a container and cooking a meal.

I think it's better to look at this from the perspective of what actually makes it less likely for animals to be harmed than to stand on the principle not matter what the effect is. Hmm, sounds like the kind of thing a Utilitarian would say.