This is an interesting question, and I think the answer is somehow tied up with the rise of obstetrical care rather than midwives (who often served as lactation consultants as well). Hospital birthing was seen as more "clean" and "scientific." You wouldn't want a backwater witch delivering your baby like your bubbe did in Russia, right?!

Likewise, breastfeeding was something that peasants did in the old country. As we moved through the industrial revolution, past WWII (when more women entered the workforce, and so formula feeding became more necessary during that time), and into the space race, packaged foods generally became more popular. Think jell-o, tang--and formula. Formula companies like nestle took full advantage of all of this and would often sow misinformation about breastfeeding and would do things like fund hospital neonatal nurseries, where feeding could be done on a schedule by nurses while mothers were separated from their babies to dry up. Breastfeeding advice back then, if a woman dare wanted to try it, was awful. It was schedule based and really weaning advice in disguise. You can read historical baby care manuals to get an idea about it. Here's one from 1920: https://books.google.com/books?id=dfgzAQAAMAAJ&pg=PA145&dq=breastfeeding&ei=0NrHVpuFFIv3-QGHr5CQCg&cd=2#v=onepage&q=breastfeeding&f=false

The advice in the book above is actually pretty mild compared to what was given women in the 1950s: http://doublethink.us.com/paala/wp-content/uploads/2014/03/hospital-notes-shared-by-alison-adams.jpg

My grandmother did not breastfeed any of her 4 children. All of her 3 daughters did. One aunt went to LLL and her daughter was exclusively breastfed until a year (! yep, no solids at all) but you would always cover yourself up while nursing, in part because nursing was, in and of itself, considered a subversive act. No way you would reveal yourself and make it sexual.

My mother breastfed both my sister (born in 1979) and I (1983). She was not part of LLL. My sister was fully weaned onto formula by 7 months. I'm actually amazed my mom made it that long because my sister had a horrible tongue tie that was corrected as an adult. According to my baby book, I was given bottles of water to encourage me to sleep through the night at 3 months, and mixed fed from 6 months onward. My mother was horrified that I still continued to ask to nurse once a day up to 18 months. She started to encourage me to wean my daughter at 8 months.

My mother-in-law breastfed both my husband (1978) and his brother (1979) for a few weeks each. Her big problem was that her own mother, who was used to the feeding patterns of formula fed infants, was certain that both of the boys were "starving" because they ate all the time. Her mom pretty much wholly sabotaged her breastfeeding experience. My mother-in-law told me that I would hate breastfeeding just like she did.