I'm a social historian, so this question is right up my alley!
Around the 1920s, society became really enamoured with all things scientific, and the knowledge about infection and germs gained in World War I made all of society a bit crazy about cleanliness and using science to protect and improve their lives. At the same time, women were taking courses in "domestic science", to teach them methodical, scientific and sanitary ways to run a household. This coincided with the discovery of many previously unknown vitamins and nutrients, and a rise in supposedly "healthful" engineered diets (the work of Kellogg comes to mind). So society's new love of science was certainly one factor in the rise in forumla for babies. Breastfeeding was unscientific, and scientists (who were, for the most part, men) saw it as dirty.
Another was a perception that only the poor breastfed (this perception was spread by advertisers and formula manufacturers, of course). If you could afford to buy formula for your child (even if you couldn't, but wanted to keep up with the Joneses) that's what you would do.
Thirdly, and ironically, the emancipation of women, the suffrage movement, and the entrance of women into the workplace (especially in World War I) resulted in a whole new marketing niche: the "new" woman, who was carefree, not tied to her house, and had an active life outside the home. All kinds of time-saving devices began cropping up for this new breed of consumer, including forumla. No longer did women have to be with their babies all day, breastfeeding. They could use forumla, and continue to live a carefree, modern life.
So, we've had almost a century of manufacturers and advertisers spreading the message that formula is a-ok. Now, I guess, they can have the further benefits of marketing to all those ff babies who grow up to have diabetes, etc.