Woo, I love other peoples drama! My sister quit uni when she was a youngster. My mother went apeshit. Years later it turns out that it was because she saw the absolute worst-case scenario and was terrified that my sister would do nothing with her life. When my sister put her alternative plans into action and showed my mother she wasn't planning on being a bum, it all got resolved. So if you haven't already done it, try and present to them something concrete as your alternative plan to show them that you aren't just "quitting".
If they do end up really down on you, don't worry too much about it. You have the rest of your lives for the ups and downs of family life. My parents have been terminally disappointed in me before now and I've been equally disappointed in them. I say it's their fault since they raised me