Has he seen the Kappa website yet? (
www.kappa.org). There is a lot of wonderful information on the website, especially in the For Family and Friends and Why Kappa? sections.
Paying the room and board for the chapter facility is really no different than paying room and board for a residence hall, and living in the chapter facility can potentially be "safer" as there are more strict guidelines as far as visitors and house rules go. The chapter treasurer should be able to give you a detailed breakdown of the house bill and where each portion goes. You'll find the majority of the money goes towards the operating costs of the chapter facility - utilities, salary for the House Director, meals, etc. The portion that goes directly to the chapter is budgeted between the chapter officers and is used for things like sisterhoods, philanthropies, initiation and educational training.
Perhaps he would be more amenable if you showed him the benefits of Kappa that last beyond the undergraduate arena? Networking opportunities, leadership, etc... With an alumna base in the hundreds of thousands, you can go to virtually any city in the US and find another Kappa. Internships, references, job openings, finding housing -- the connections you have as a member of Kappa can help you with almost any aspect of your post-graduation life.