I’d say the case is more easily made when the competing school differs in size, structure or overall environment in comparison to a school like Penn. If you wanted a smaller school in the country, for example, then you could articulate your position based on your personal preferences. If you simply want a school that’s “not Ivy,” that’s roughly as arbitrary as wanting “only an Ivy.” So if you like Vanderbilt, first define for yourself, and then try to explain to your parents, what it is you find particularly appealing about the school.