If you add sugar or salt, or even sand, to soda water, it fizzes violently because you have added what we call nucleation centres, places where the dissolved gas can easily leave the solution. Clean water does not contain many nucleation centres, so it takes longer to fizz, and will fizz for longer.

Milk contains more nucleation centres than water, so the dissolved gas escapes almost immediately.

Also, milk froths more than water does, so the gas that does escape does not all go free at once, but remains in the bubbles, turning most of the milk into a froth that can be quite a nuisance, or quite pleasant, depending on what one wants.