I never roll my eyes. That's true. It's because I'm afraid they might fall out. That's only partly true.

But my wife frequently rolls her eyes -  especially when I say something. It's not because she is annoyed, though. It's just disbelief.

Sometimes we roll our eyes when we find something is difficult to believe.

For example, if someone told you something that was really hard to believe, you might roll your eyes.

I don't think people roll their eyes when angry. Angry eyes look like these eyes:

https://www.shutterstock.com/search/angry+eyes

The same in Russia. 

As Richard said - it can be also if you are surprised /can't believe in something.

 I think it can be a sign of threats as well.