In A Doll's House, how does Torvald define the role of women?
Torvald represents a fairly typical attitude in 18th and 19th century Norway and across Europe. Even well into the 20th century, a woman could barely exist outside her husband's house, after leaving her father's house. She was defined by her husband and although she fulfilled the role of homemaker, such as Torvald presumes of Nora, she was incapable of making decisions of any importance.
Torvald holds a respected position in society and is stereotypical of his era
male dominated, authoritative, and autocratic.
He makes rules for his wife, not just the children, to the point that Nora behaves like a child when she is caught "stealing" sweets, namely macaroons. Torvald continuously demeans Nora, his "little squirrel."
Ultimately, this attitude will be Torvald's downfall. When Nora's deceit is revealed, he sees it as a betrayal and worries about his reputation rather than his marriage. Calling Nora a "hypocrite" he cannot see the same in himself as it is beyond his understanding that a married woman could behave in such a way. He is not concerned with her motives.
To the end, Torvald does not realize that he is in the wrong and he is disconcerted by Nora's reactions. He cannot understand anything out of the scope of what he sees as society's accepted norms.