Perhaps they don't think getting a liberal arts degree is all that stupid, perhaps they think that paying 30K a year or ($120,000 for 4 years) is stupid when you have to borrow to get it.
Advertising design isn't ONLY offered at private schools. lol It's called marketing, advertising, design, etc at other schools. If you have found this major and its "exactly what you want and only offered at X school in the country" then its obviously not a well sought after career. Think of the rules of supply and demand here and look at many schools in your state.
You CAN borrow money in your name when you apply for fafsa regardless of how high your folks income is. However you do not get to borrow more because you have chosen a high cost school. Freshman dependents can only borrow 3,500 per year in Stafford loans. (Which is why state and community colleges are so popular)
If you really have your hopes set on this school and want further funding to go, your best bet would be to talk to this school and find out about their scholarships. I'm sure you aren't the only one who doesn't have 30K laying around. If the school can't offer you the option on going with federal student loans and scholarships (without resorting to private student loans) then you need to find a better school.