I get what you're saying, twilight , I really do. Yes, I would pause before drinking a cat's milk milkshake, for the very reasons you outline. Being confronted with cat's milk or kangaroo milk would force me to actually think about what I'm drinking, whereas drinking cow's milk is so normalised that I do it without thinking too much about it. That doesn't mean it's less 'ewww', just that I've been conditioned not to think of it in that way. I understand that fully.
That said, I still know that I would drink kangaroo(or whatever) milk long before I would ever contemplate drinking human breastmilk as a treat.
The reason has less to do with the substance of breast milk (on that point, I would have to concede that it must be more suitable for human consumption than the milk of another species), and more to do with my concept of personal boundaries and social appropriateness, as I said above.
Whether for biologically-, culturally-, or socially-driven reasons, and rightly or wrongly, when we consume the bodily products of animals, we are not in communion with them, we are using them as things for the production of meat/milk/eggs. That's why some people (understandably) have such ethical problems with eating meat and animal products.
But most humans relate to other humans in a much different way than we relate to cows or kangaroos. When we share something of our bodies with each other, it tends to be an intimate and emotionally loaded act.
A large part of what made breastfeeding so special for me (and a large part of my distress when I struggled with it) was the sense of intimacy it gave me with my daughter. my milk , from my body , nourishing my child. I felt a similar awe at the extent to which she and I were bound together when I felt her move inside me during pregnancy.
I do not think of having a glass of milk as an intimate act with the cow who produced it, because I am not a cow (am I walking into something here? 
). Eating ice cream made from the milk of another woman, though, would feel like far too intimate an act for me to be comfortable with it.
I accept that by the logic of my own argument, it would probably be a more ethical act to eat ice cream made from a woman who willingly shared her breatmilk, than it is to eat ice cream made from a cow who was used as a means to an end against her will. For that reason I envision myself giving up dairy, but it doesn't help with with the social boundaries problem.