Tread lightly now as it seems likely to me that you will encounter further difficulties in coming to an agreement with your father in the future.
That means, find a compromise. Many of the posters above have suggested majors that would be similar to but not economics, and you will be able to pursue your goals, as you believe them to be currently. The good thing about having an undergraduate degree in many of the areas mentioned is that you will develop critical thinking skills useful in any career you chose, inciuding finance.
How you use those skills to further your goals is what counts. You will also need to consider what sorts of internships or intermediate jobs and research, while you are still in school, will help you to further those goals.
Do go to career services or find an academic advisor who can help you define your path and connect you with the support you need. Is there a Muslim student association or women’s group at school where you can find support amongst peers? NYU is a large and diverse school so you should be able to find likeminded persons from a similar background or set of circumstances with whom you can commune.
Also, I was wondering if your mother has input here, as you have only mentioned brother and father.