Basically, I find it disgusting because I think it is unnatural, and I use unnatural in the sense that there is no human tradition for this. It's just weird and disgusting in a visceral way.
Also, I don't know if I would be okay with drinking a koala bear's milk, for example. I'm accustomed to cow milk; I'm not sure about other animals.
You're defining "natural" in an odd way -- as tradition. "Natural" should mean the way nature intended, and there's no way nature intended for humans to chase down pregnant cows and squeeze out the milk they're producing for their babies (there was a really funny line in Burmese Days about this -- something like "if you want some milk, we can chase down a cow for you".
At least human milk is intended to be drank by humans, albeit at a certain age.
<edit> that being said, there's a certain relationship between a mother and her nursing children that is very important psychologically. So drinking the milk of somebody who isn't your mother is, I'll agree, kinda gross. But we take that relationship away from animals unfairly and drink THEIR milk, so...