Well.. that truly is the big picture. Because it ignores a lot of the finer details.
Let me start by saying I really don't care what I eat. Someone who habitually consumes as much snack food as I do does not have the luxury of a high horse when it comes to this stuff, and generally if it looks like food I'll eat it.
That being said you massively oversimplified GMO and the inherent dangers. Yes, selecting traits and genetic variants has long been a practice amongst the farmers of the worlds, and there's nothing inherently wrong with it. All right, it kind of sucks for the cows who literally cannot survive without constant human supervision, but it all tastes the same on the dinner plate.
The problem with GMO isn't the selection of specific traits. It's that, largely, it's a very new science with very little understanding. Just because we can map a genome or two doesn't mean that we know the entire cause-and-effect of genetic modification. We're still learning a great deal about what each gene affects, and even in the simplest of genomes this can be a long and complicated process. Cows are not simple. Certain plants are, but that's a different aside. The problem is that since we don't exactly have the firmest grasp on the subject matter yet, we're hardly equipped to regulate this practice for consumption. Yet we claim that it's all very well-controlled, which it isn't really. We don't know exactly all the ramifications, we simply know the most superficial results: more tasty food that doesn't immediately kill people when they eat it. This, too, is not a new problem in food regulation, but GMO is a very rapidly evolving practice and as such is hard to keep up with. So, naturally, people are reluctant to consume the most basically engineered foods.
Then there's the knowledge that there quite literally is food that is becoming hybridized with other foods that it couldn't otherwise naturally fuse with. Like pork with fish genes introduced to produce omega III fatty acids. Or the numerous fruit fusions such as pluots(plum apricots) and lematos(lemon tomatoes). These all sound pretty awesome in theory, we admittedly know very little about the results other than instant death, disease, or sterilization are none of the side effects. People are afraid of another asbestos: a seeming miracle product that will save the world right up until we find out about the cancer. And a little caution never hurt anyone, least of all science. If people like us are fine with eating from the genetically modified tree of knowledge, that's all well and good. But to simply quack "paranoia" at everyone who shows a little trepidation towards eating pork carrots(OK, an exaggeration, but still one with a point) doesn't exactly demonstrate a grasp of what the greater problem is here.
In addition to this we don't know of the potential allergens we may be creating through entirely new foodstuffs. Most of these things have never existed in nature before, and to make so many new kinds of food now carries the risk that certain people simply won't be able to consume it and won't even know this until their esophagus closes up.
More to the point, GMO carries other risks more tangibly. The introduction of stronger, modified products often results in the destruction of the untampered product. This is more easily controlled in animals, but in plants it's an absolute nightmare to keep under wraps. Just look at how many poor farmers companies like Monsanto sue because they happened accidentally have their crops infested with runaway spores and seeds from their GMO crops. This introduces massive legal confusion, and also makes it difficult for the "paranoid" to select crops that didn't start in a petri dish. Whether or not it actually is dangerous to consume, GMO is forcing itself out there against the will of the farmers and the frightened and uneducated masses.
Bottom line, GMO may be the savior of humanity(more efficient crops, healthier meat, awesome flavors), but we have no real way of knowing the effects, and thus people are cautious to embrace it. This isn't an experimental car or something, it's what we eat: a very tangible concept that hits pretty close to home for everyone. If all of a sudden someone introduced a new element into oxygen that survived the constant process of filtering in plants and animals and supposedly enhanced the performance of humanity, that would sound super-awesome, but we might still be reluctant about releasing mass quantites of that element into our air without a little more testing.