Why should we take out a loan to send our daughter to a private college out of state?

My husband and I have been happily married for 14 years, and we have 4 kids. Their ages are 17, 12, 11, and 11. We are retired military, and disabled vets. We are college educated, and we have decently paying jobs/professions. We live in a mortgage free home, and we don't have any debts whatsoever.

Our 17 year old daughter has started to look at colleges. The college she really wants to attend costs about $29,000 a year for book, tuition, room and board. She won't qualify for any kind of Pell grants, because my husband and I make too much money. But I believe she can get student loans. She doesn't want to get any student loans, and she's expecting us to foot the bill for her entire education.

We've already told her that we're more than willing to send her to an in-state public school, but were not taking out any loans. She thinks that we're being unfair. We think that she's being unfair to us, when we still have 3 more kids at home to take care of. We want our daughter to have a college education, but we're not willing to put everything on the line for her.
Added (1). @ D, she took a tour of this school with her best friend last fall. She fell in love with the school, and believe me it's an excellent institution. We have told her that we can't afford to send her there, and she keeps asking us to take out a loan for her to go to school.
We've said no, and we're not going to change our minds. I wish she would accept it, and go to an in-state school.

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