Earlier quoted context omitted.
"Why are you so angry" in native English is not a question; it's a question tied to an implication. The question implies that the person being asked the question is angry. Most answers involve accepting the implication as correct. The stereotypical example used to demonstrate this in English is probably 'have you stopped beating your wife'. 'Yes' implies that you have a wife and you used to beat her; 'No' implies tha…
I'm aware of it being tied to an implication, but I don't agree with you that "why are you so angry?" is in the same category as the example you gave ("have you stopped beating your wife"). In my view, if I ask you "why are you so angry?" I perceive you as being angry.
If you want to ask a question about the reason for the facts on which you make that inference without telling someone how they feel, you ask the question about the reason for the facts, rather than asking them to explain a mental state that you have inferred about them.