well, if your parents think that "computers are computers" (whatever that means) and if that's the main reason for not buying you one... maybe they just don't want you to own a computer, and that's what macs are.
If they think "computers are computers", show your mother an iMac or the white MacBook. Not the black one. Not the MacBook Pro or the MacPro. That might do the trick. Show her the iMac and say what a nice looking monitor it is. Then ask her to look for the computer. When she can't find it, point to the iMac - THAT's the computer!
(MacPro and MacBook Pro usually work better with dads, but you know your parents better than I do).