To avoid getting in too deep on the science let's look at it using a holistic view. Many GMO crops are designed to resist herbicides. Some of them also produces pesticides so that if a certain bug eats them it will kill them. Now personally I don't want to eat something that can produce a pesticide, and I don't want to feed it to my food.
Many countries around the world have an outright ban on GMO foods and many more have restrictions and labeling requirements. One of the reasons that these bans are in place is that people are uncertain of the possible health effects. Reports from one side say that they are unhealthy and reports from the other side say that they are healthy. The problem with much "science" these days is that it is based on who pays for it. However, much not for profit science that is not funded by big ag will have results showing that it is unhealthy. Click here for a good article that gives some of the reasons to avoid GMO.
Here is what I know as a farmer and consumer looking at the anecdotal evidence. My animals seem healthier on non-GMO feed. They produce better products. Food was not modified, except for selective breeding, for thousands of years and it worked for them and it will work for me. Many other farmers report having better crops and healthier animals when using non-GMO feed. I am inclined to listen to years of experience and wisdom, because they are the ones with their hands and eyes on the food everyday.
We have been given this blessed planet with many great plants and animals on it. Since God gave us dominion over it all we need to be the best shepherds of this resource we can. I believe that using what is natural and created by God is the way to do that. In the course of that I hope to produce the best food possible for you and my family.
"If you are willing and obedient, you shall eat the good of the land" Isaiah 1:19