Why was Torvald so upset when he found out that Nora had borrowed money to save his life in A Doll's House by Ibsen?

Torvald's anger would be justified within the context of the social norms and expectations bestowed upon women at the time the play takes place, which is the 19th century. According to the standards of the time, Nora would have been expected to be an obedient, subservient wife who abides by all the rules of decorum and propriety expected of her. 

This being said, the loan that Nora makes, despite her good intentions,  breaks with every rule of spousal behavior that Nora would have been expected to follow in these ways:

• Nora makes the loan agreement behind Torvald's back. Even Linde tells Nora that it is impossible for a woman to initiate a transaction of this nature without the consent (or signature) of a husband. That Nora breaks this major rule is something to be concerned about, either way.


• Nora made this loan with Krogstad, who is a disgruntled employee of her husband's, and also an insubordinate.


• Nora is blackmailed by Krogstad, and Torvald finds out that now they are at the mercy of the man.


• Torvald realizes that his reputation as a man, as a supervisor, and as a husband will now be in peril. He will be looked upon as "weak," and as someone who cannot "control his home."

The problem is not that Torvald was angry at Nora; the issue here is that he gave more importance to his anger than to the fact that Nora had made so many sacrifices to save his life.