Vegans seek to avoid using animals for food, clothing, or labor, as much as is practical. In modern industrialized farming, as we have in the United States or much of Europe, dairy does indeed involving killing animals to make milk profitable. It also involves alot of potential large environmental externalities or costs.
Now days we tend to use the term "vegan diet" to refer to diets that exclude animal products, but Veganism itself as an ideology or philosophy is an ethical movement that started in England in the early 20th century.
There are actually some vegan dairy products out there now, at least in the US. They are made from whey protein produced by genetically modified yeasts, similar to fermentation. However, making vegan or non-animal whey can be done alot more cheaply than so-called "lab grown meat", and it's a far simpler process. Some Vegans consume non-animal whey here in the US, but others don't. I have tried a few, out of curiosity. Some taste decent, others just taste too much like dairy and are very greasy or fatty, like whole milk (usually they are made with some kind of vegetable oil to keep saturated fat lower than actual dairy milk). I no longer have much of a taste for dairy in general, and some of these products are quite high in fat.
Most of these products are being sold in health food stores or upscale groceries, and are marketted towards environmentally conscious consumers and vegans who are drinking them as protein supplements to support athletic goals.
And if you are interested in health, there might be reasons to avoid or restrict whey consumption, regardless, as it tends to have more branch chain amino acids. While these are hypothesized to have a more anabolic (tissue-building) effect, and are widely consumed by body builders as a result, excessive consumption might also contribute to cancer cell proliferation. Non-animal or vegan whey also isn't really a "whole food", and has to be part of a heavily processed product, which again, some people don't like based on the particular dietary philosophy they adhere to.
On a side note, another reason I prefer plant milk over dairy is because I have found plant milk stays fresh in the fridge alot longer. I never have the experience of picking up a carton of soymilk and getting a whiff of something rancid, something that happened too often with the kind of cow milk we have in the US.