Read this: http://fooledbyrandomness.com/pp2.pdf and before making arguments, make sure your argument hasn't already been responded to in the "Fallacy" section.
Of course, there are many non-scientific arguments about GMOs. I'm not talking about those.
EDIT: Someone asked for a tldr. It's a useful skill to learn how to read a paper (start with the abstract and the conclusion), but I'm pasting the conclusion here anyway:
This formalization of the two different types of un-certainty about risk (local and systemic) makes clear when the precautionary principle is, and when it isn’t, appropriate. The examples of GMOs and nuclear energy help to elucidate the application of these ideas. We hope this will help decision makers to avoid ruin in the future.