Why does Nora resolutely leave home in A Doll's House?

Nora leaves her family and home with absolute resolve because she realizes that she has no individual identity there. 

At the end of Act III, Nora tells her husband Torvald

NORA: Our home has been nothing but a playroom. I have been your doll-wife, just as at home I was papa's doll-child.

In evaluating Nora's actions, it is paramount to understand that Ibsen meant to shock his audience into an awareness of the repression of...

Nora leaves her family and home with absolute resolve because she realizes that she has no individual identity there. 

At the end of Act III, Nora tells her husband Torvald

NORA: Our home has been nothing but a playroom. I have been your doll-wife, just as at home I was papa's doll-child.

In evaluating Nora's actions, it is paramount to understand that Ibsen meant to shock his audience into an awareness of the repression of women at the time this drama was written. Therefore, in this context Nora has no choice but to leave her husband and family if she wishes to possess any autonomy. She can only find her self-identity outside of this environment:

NORA: I have other duties just as sacred. . . duties to myself. I believe that before all else I am a reasonable human being . . . or, at all events, that I must try and become one.

Ibsen's play illustrates the tragedy of womanhood and motherhood in his time; that is, many women were tragically bound to domestic roles and had few outlets of individual expression. (Nora's surreptitious eating of the macaroons symbolizes her attempts at individual expression.) Even when Nora has acted out of love as an individual in procuring the money so that her husband could go to Italy in order to restore his health, Torvald scorns her loving action because she broke a law in saving his life. 

Of course, this revilement by her husband becomes a defining moment in the play because Nora then makes her decision to no longer be but a "doll" who is manipulated by others. With resolution, she departs alone, for she must be solitary if she is to find any self-expression and autonomy.