Robust to accepting responsibility
her arrogance is overarching- this is clearly irony as she juxtaposes what would be executed of someone in a charitable position.
Mrs Birling uses her power to benefit her and she saw Eva Smith as someone trying to mock her and felt attacked.
The noun"duty" cause be a tool on showing how for capitalists upholding the class system was paramount and their duty
For Mrs Birling, her duty may be to uphold the class gap by refusing Eva's help