In nature, different species cannot mate. There is a natural protection against the mixture of these traits. When a gene from a fish is put into the DNA of a tomato, the DNA is fundamentally altered, creating a completely different unnatural plant. The effect genetic engineering has on human beings and the environment is unknown. It's never been tested on either.
Genes generally do a lot more than just one thing.
One gene can be responsible for many functions. We have no idea what 97 percent of DNA does. It's not difficult to imagine that there may be unexpected outcomes with fundamentally altering something we basically know nothing about. There are major concerns from the scientific and religious communities about this technology. Research has documented cause for these concerns.