Obviously there's some just crazy to the anti-GMO side, but I'm gonna try to just play some devil's advocate and outline some of the legitimate concerns. Although I think a good scientist will come out with a more fair understanding of why. This will be long but I'll try to write in a magazine style.
It sounds scary. Especially when we go oversimplifying things. The classic being when pro-GMO people tell others "it's the same thing we've been doing for years." Transgenic splicing through plasmid vectors is not the same thing as hybridized breeding, nor is it even close. I truly wish people would stop using this argument, it's pure shit. Process does matter. Powder coating is not the same thing as anodizing just because both can add a surface color to metal.
There's been a growing concern of what is actually in our food and what we tell people about it. Some of this is pretty legitimate. Way too many things get pushed on food labels as "natural ingredients" for instance, and while safe they can be pretty gross. (and yes, anal glands from Beavers are pretty darn common in food, and this is just one example). While yes it's bad buisness practice to suddenly slap a big "GMO!!!!" label on food, it doesn't mean it can't be tracked. The FDA came out and now requires a scannable barcode on every medical device for traceability, and they gave 2 shits about the business impact it would have. I see zero reason why this could not happen in food too (barcode/QRcode leads you to a database where you can see where food is from, processes used for creating it, shelf life expectancy, ect.). All the arguments I hear against it basically boil down to pro-GMO people acting for good PR for food corporations. And I think that has been something the food corporations have pushed hard to get pro-GMO people behind them on. In my opinion, if you're a scientist or engineer, you should NEVER be for hiding information and facts. You should stand behind the product and the processes used to create them.
Flint water, Fracking story X, poisonous mine/quarry/industry drainage GM recalls ect ect ect. There's a story of every few months about a massive failure of science and engineering that we did not anticipate, design for, or properly accommodate. A lot of times it's more on the money or regulation side, but that doesn't matter to a whole lot of consumers. They just want to trust a product, and there is some legit worry GMOs will go the same course over time where a company gets greedy, regulations get lax, and the end result has a huge impact.
The FDA is way more lax about food than sectors like medical devices or pharmaceuticals (and there's still tons of issues in those 2 health sectors). Food for thought though, in Asia raw eggs are pretty commonly eaten and of course not in America. The thought around this is that's because regulations in Asia are much more stringent; because people eat raw eggs all the time. Here the regulation matches the need and it does pretty good, but in reality it could be much tougher. Just look at how much food labels have changed over the years, there was a time you had even less information by far into what you're ingesting and at the time that was considered great. Lately companies have been getting away more and more with calling something a supplement or cosmetic and getting away with it. This all goes to confusing the consumer, and causing more distrust.
Dismissiveness by the pro-GMO side of everyone as as a loon/crazy/hippie ect. That shit never helps, and it makes people feel like they need to defend themselves.