Americans are prudes when it comes to breasts. You can definitely see our Puritan roots. 
I wonder if anyone has done any research on the health benefits of breast-feeding beyond one year (which is what most pediatricians recommend). I wonder what physical and/or psychological benefits mother and child gain from extended breast feeding.
I don't particularly have a problem with discreet breast-feeding in public - babies have to eat, too, after all - but I'm not sure you could discreetly breast-feed a three-year-old. I always figured that once a child can actually say "Mommy, give me milk," the milk should probably come from a sippy cup, not a breast. But that's my opinion.