Why does torvald make such a decisive show of mailing the letter firing krogstad against nora’s pleas?

To show superiority and authority over Nora.

Explanation:

Nora, Torvald, and Krogstad are characters in the play "A Doll's House", by Henrik Ibsen. Torvald and Nora are husband and wife, and they a very sexist and abusive relationship. Torvald regards Nora as inferior, dependent, incapable. He sees himself as her lord and savior. To his mind, Nora must do everything to please him since, without him, she would be nothing. When Nora begs him not to fire Krogstad - who is blackmailing her -, Torvald gets upset. He will not let a woman tell him what to do, even if she is asking, like Nora is, in a submissive manner, promising to entertain him. He makes such a decisive show of mailing the letter firing Krogstad because he wants to make sure Nora knows her place. He wants to show his superiority and authority over his wife.

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explanation:

a low four-wheeled open carriage of a kind formerly used in russia.