MSG contains glutamic acid, which is what causes things to taste savory, a flavor known as "umami." Umami is a major flavor profile in a lot of asian foods. In the USA it was difficult for people cooking asian foods to get their hands on natural sources of umami that are traditionally used, so a lot of asian restaurants, specifically Chinese restaurants, started to use MSG to get that savoriness. MSG was really not used in the USA or Europe to that point, Julia Child's The Joy of Cooking famously called it "the mysterious white powder of the Orient.”

In the 1960's and 1970's articles came about about how MSG could give people headaches or have other negative effects. Someone wrote a letter to the editor of the New England Journal of Medicine saying "hey, when I eat a bunch of Chinese food I have these symptoms, and some other people do too, and we think that it may be connected to overconsumption of MSG." This ended up turning into a New York Times article called "Chinese Restaurant Syndrome Puzzles Doctors," which blamed MSG. The story took off and people blamed MSG for a number of things.

There were some studies claiming to support these conclusions that MSG was dangerous, but they were all deeply flawed and later debunked. For example one of the most notable ones, a 1969 study in Nature by Dr. J.W. Olney, concluded that young mice who had a highly-concentrated dose of MSG injected directly into their brains experienced markedly higher rates of obesity and even tissue death. The issue is that (a) the concentration of MSG being used was significantly higher than normal consumption and (b) you eat MSG, you don't inject it into your brain. That study, like just about every other on the dangers of MSG, was debunked.

There have been a number of studies done showing that MSG is not dangerous at all, nor does it cause this "Chinese Restaurant Syndrome," but the public perception already existed that it was bad, and changing perceptions is very difficult, so a lot of people continue to think that MSG is inherently bad, even though it is not.