There are two main reasons for which many people oppose the creation of genetically modified organisms (GMO) and their use in food. First, there are people who oppose these kinds of plants for health and safety reasons. Second, there are those who oppose them for environmental reasons.
Many people feel that GMO foods are not safe for human beings to eat. They believe or fear that there is something about the process of creating GMO that changes the foods and potentially makes them dangerous. They worry about things like allergies and they worry about unforeseen impacts on the nutritional values of the foods and on their general nature.
Second, many people worry about how the environment will be impacted by farmers growing GMO foods. They worry, for example, that the GMO plants might cross-breed with other plants, creating all sorts of plants with unknown qualities. In addition, they worry about the loss of biodiversity. They feel that GMO plants will come to be the only plants grown, thus reducing the amount of biodiversity in the plant world.
These are the main concerns with raising GMO plants. For other issues, from the point of view of an anti-GMO group, follow this link.