I am writing an argumentative essay in which I claim that GMOs are safe. I know, it is not proved, but for the sake of my course I want to prove it. The counterargument that my professor said to me is that genetic modification is not like selective breeding. GM brings changes faster and most of the cases it is inevitable. We don’t know the consequences and they can be bad. On the other side selective breeding is changing the organism slowly and something bad can be prevented in the start of its development. What are disadvantages of selective breeding to compare with genetic modification? Can I use the mutagenesis as the example of selective breeding and use its cons?
Yes, GMO are safe to consume! See Is Genetically Modified food safe to consume?. Now, there are other (potential or real) issues related to the use of GMOs such as for example a loss of genetic diversity if every farmer plant the exact same strain. Talking about such issues will require talking about ethics, economy and sociology and it can therefore not be answered in a science website only.
Your teacher's argument does not make much sense (although a direct quote would have been helpful). GM plants also have to develop. They are organisms too!
[W]hat are disadvantages of selective breeding to compare with genetic modification?
Keep in mind that it is practically impossible to define GMO. Many of the things that we would call GMO actually don't result from much more than just selective breeding. Following this logic corn, wheat, sunflower oil, lettuce, broccoli, cauliflower, peanuts and pretty much everything else you eat is a GMO.
Attempting to let aside the semantic issue a comme argument is a lack of lack of familiarity and this is why extra precautions and testing must be done. See What risks exist with GMO, but not with selective breeding?
can I use the mutagenesis as the example of selective breeding [..]?
Mutagenesis and selective breeding are two different processes (although often used together). One is not an example of the other.