In today's accounting environment most public accounting firms require an employee to have a credential like passing the CPA exam and being a certified public accountant before that person can move up into a management role in the company. In order to be eligible to take the CPA exam, a person must have at least 150 eligible college credits to sign up. In order to accumulate that many college credits most people find they must have an advanced degree like a Master's degree. When applying for a Master's program, a fair number of schools do not want the applicant to have an undergraduate degree in accounting. An undergraduate degree in accounting does give someone a broader base of accounting knowledge, but it does not necessarily qualify them to work toward a Master's degree at certain colleges and universities.
So my advice is to check out your options and see what is required if you want to get an advanced degree. We hire people with all sorts of undergraduate degrees that are unrelated to accounting but if that is the path taken, a Master of accounting or comparable advanced degree would be required.