OP, while it would be better to be coming out of Stern to get into consulting or I-banking, both fields are primarily looking for the best and the brightest, and your major doesn’t really matter as much. You just need to graduate from a top school (check) and have a top GPA (up to you over the next 3 yrs). That said, so that I do not lead you astray here, you should check with career services and see whether your target types of companies recruit at CAS as well as Stern. If not, you may want to seriously consider a switch, as Stern is one of the top UG business schools and will probably provide you with many different opportunities in business if you do well.
In Stern, you could also explore a major in operations, marketing or management instead of finance to try and deflect the whole interest thing, but I’m guessing none of that would really appease your father too much. Those majors may even be more desirable for consulting, but again, they are really looking for smart people so find a major where you can do well (preferably something you enjoy).