Where to put state of research in thesis when it needs to be referenced in introduction?
General background is a normal component of a thesis, typically more so than in research papers in the field.

You should follow your supervisor's advice for two reasons:


They are an expert in your field, and you (should have) chose them as a supervisor for this reason. If you don't value their opinion, you have made a serious error in making them your supervisor.
They will be evaluating your work and will be the one (or part of a small group) deciding whether your thesis is acceptable.



  This really irritates me because I always discussed the state of research later on after giving basic theoretical backgrounds needed for understanding (this would not be possible when mentioning state of research in the introduction)


This statement makes absolutely no sense to me. This sounds like exactly what your supervisor is recommending: giving basic backgrounds, then discussing the current state of research.


  I also do not think that generalizing the problem so much that it is not needed to use basic technical terms when defining the research question is useful at all.


This might be your opinion, but it seems like your supervisor wants your thesis to be at least somewhat readable by someone not intimately connected to your field. That's pretty typical advice in an academic context, especially in a thesis.