Vegan means no animal products at all. The farms can say the animals are treated humanely all they want, but that doesn't mean it's true.
Milk production can't be at all pleasant for cows. The cows are usually artificially inseminated on "rape racks" and separated from their calves hours or even minutes after giving birth. For the next two to five years of their lives they're kept in cramped quarters and they get to have they're boobs yanked on 2-3 times a day. When their milk production starts to wane, they're slaughtered. The very rare, small, family-owned farms, like the one my grandparents used to have :-( , treat the cows slightly better, but they still seem pretty miserable.
An ingredient in cheese is the rennet in calves' stomachs. The calves, of course, have to be killed for this to be obtained.
The production of honey causes the deaths of millions of bees. Most people seem to think we can overlook this because bees aren't cuddly, but most vegans still think they deserve the right to life and freedom.