Technically I have nothing against breastfeeding in public, and I support it fully but I do understand why some people could be offended or put off by it, so I would also argue that it should be a courtesy to do it privately. The breast is seen as, not just an organ for feeding, but also as a sexual organ (Which is a separate debate) Even though the woman has every right to breastfeed in that public place, it can be embarrassing for other people and, perhaps, even embarrassing for the mother.
Many women try to do it discreetly and cover themselves with a cloth or blanket while their child feeds. I do not know why it would be embarrassing people were once all fully nude and thought nothing of it. Even though we have evolved from that many women wear clothing that barely covers them and seems more like undergarment. Why does no one feel embarrassed of this? Why does no one tell them it's disgusting and should only wear that "in private?"
Yes, many people try to do it discreetly, but many people know what they are doing and, so, feel embarrassed. Yes, we were once naked, but at that time we did not have to contend with embarrassment in the way we do now. As I said, the breast is seen as a sexual organ. As to the "revealing" clothes people choose to wear, you must remember that these people may choose to wear these clothes but as soon as they took it upon themselves to strip naked, they would refuse because of embarrassment. Women who breastfeed in public are not revealing themselves in a sexual way, therefore its embarrassing to other people because it feels as though the woman is making herself vulnerable. And, in a way, she is, because breastfeeding in nature is a very dangerous time for the mother and the young due to predators who will use this lull in the mothers concentration to attack. Its a natural feeling, and people want to avoid it and so they ask that breastfeeding be done privately. However, I disagree strongly with your comment on it being considered disgusting, it is not disgusting and it is merely a vocal minority of people who would say that it is.
It should be up for the mothers to decide. If they feel uncomfortable and vulnerable in public they can do it in private, but if they feel the need to do it while in a public place they should be able to without people staring and telling them to do it in private. If people do not like it they should just look the other way. I personally do not feel that anyone should feel embarrassed knowing a woman is feeding her child the natural way rather than using the formula. As for the style of clothing, I am personally against the tight and lack of clothing the women wear, but even if you aren't if you are ok with one woman wearing a shirt that barely covers her then you should be ok with a mother feeding her child for a while.
While in theory, and in a perfect world the idea that a woman was to breastfeed without causing themselves or others embarrassment would be pro and undisputed. Logical even. I agree, breastfeeding should not be considered embarrassing, yet it still is for many. Yes women should be allowed to breastfeed in public if they wish, as long as they respect other people's feelings in the same way as they should her privacy. It is using an organ which is otherwise sexual in a place were everyone can see, or assume and it may simple be uncomfortable for a person. This is not a fair position to put someone in. In a much more extreme way, the use of disturbing images of abortion in an attempt to change peoples views is similar. While the people have every right to show said pictures, does that automatically mean they should? Because said pictures could shock young people and children. That is a very extreme example, yes, but in a smaller way the same principle exists when breastfeeding in public. That being said, Women should have the right to breastfeed were ever they need to but a private option should be a priority because you do not know how people are going to react.
I find the act of breastfeeding extremely intriguing, yet I still find it awkward when a female family member bares her breast to feed her baby, and should I feel embarrassed? Yes I should because the embarrassment makes me give her the privacy she deserves.