She tried to understand why, despite the fact that people want to be good, compassionate and good-natured, still, out of nowhere, appear irritability and hostility.
Yes.
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I'd remove the comma after 'still' and the comma after 'nowhere'.
I'd also consider reordering the sentence structuring like eg this.
She tried to understand why irritability and hostility appear out of nowhere, despite the fact that people want to be good, compassionate and good-natured.