Why are "genetically modified foods" getting all kinds of push back from many sides including the EU?

Genetically modified foods are becoming more and more available. Most of the modern foods are modified provide more and better product such as rice, corn, wheat and now even salmon have been modified to achieve market size faster that before. The published complaints seem to suggest that these foods are somehow tainted and there is no knowledge of future problems. Besides, the modifiers are large multinational corporations that have evil intent.
But hasn't mankind always been modifying something. We took a wary wolf some 10000 years ago and now we have toy poodles. Wheat, corn, rice are not like today from what it was just a few hundred years ago.
In the past, breeders/botanists would make multiple generations to get the desired results. Today, technology can make changes is one or two replications.
Could these GMF cause hair to fall out or some serious medical crisis and how do we know that? Or is it just the fear of change?.