Just to speed up your life, Feministe has outlined the more idiotic arguments against public breastfeeding.
Here are the tired, stretched-out, armpit-stained arguments that won’t fly:
1. Breastfeeding is comparable to pooping. One is food at the beginning, the other is food at the end. One has everything the body needs, the other is everything the body has decided it doesn’t need. Changing a diaper != breastfeeding. (Also, public sex != breastfeeding.)
2. Breasts are sexytime. For some people, necks and knees and earlobes are just as erogenous as breasts, and yet we’re allowed to walk around in shorts and boatneck tops. And unlike the aforementioned body parts, breasts can be used to feed people.
3. Breastfeeding is a private, intimate moment between mother and baby. And dinner is a private, intimate moment between me and my cheeseburger. Breastfeeding = hungry baby + accommodating, lactating woman. Which is not to say that breastfeeding isn’t intimate–and natural and beautiful, too–but it’s also functional.
4. Breastfeeding should take place in bathrooms. Generally, private, intimate moments in public restrooms are frowned upon (and that’s a mistake you only make once–sorry again, Georgia Dome!), but apparently it is appropriate to feed a helpless infant in a place where people are pooping.
5. Moms can always pump or use formula. Not every woman can pump, not every baby will take a bottle, and even then trying to schedule the pumping and the feeding and the toting of perishable bodily fluids can be a hassle.
6. Ew, I don’t want to see that. Yeah? Well, I don’t want to see your FACE.
via Extreme Debate Makeover: Public breastfeeding edition — Feministe.
Life of refinement 
There is never a public uprising when women’s breasts displayed on magazine covers and billboards. But the moment we look at breasts as functional as opposed to sexual- society can’t take it. Suddenly a woman’s breasts are offensive to people, and she is shamed into feeding her infant in the same room that is reserved for defecating. Its really sad how over sexed our society is- people can no longer make the distinction between the sexual and functional breast- so they reject the functional altogether.
I agree with your comment. I would only add that it is a shame that women’s bodies become split in this manner. It is the determinism — the notion that someone’s body is USED for either sex or motherhood that really jams us up.